update

#beamerthemeOhsaki.sty#

@@ -0,0 +1,76 @@
+% -*- LaTeX -*-
+% 
+% 
+% Copyright (c) 2011, Hiroyuki Ohsaki.
+% All rights reserved.
+% 
+% $Id: beamerthemeOhsaki.sty,v 1.2 2011/11/07 22:20:32 oosaki Exp oosaki $
+% 
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120111-impact.org

@@ -0,0 +1,169 @@
+# -*- Org -*-
+# 
+# 
+# Copyright (c) 2010, Hiroyuki Ohsaki.
+# All rights reserved.
+# 
+# $Id: 120111-impact.org,v 1.1 2012/01/12 02:56:04 oosaki Exp oosaki $
+# 
+
+#+STARTUP: beamer
+#+LATEX_CLASS: beamer
+#+LATEX_CLASS_OPTIONS: [compress,dvipdfm,12pt]
+#+OPTIONS:   toc:nil
+#+BEAMER_FRAME_LEVEL: 2
+#+BEAMER_HEADER_EXTRA: \usetheme{Ohsaki}
+#+BEAMER_HEADER_EXTRA: \usepackage{palatino}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\sfdefault}{ppl}
+#+BEAMER_HEADER_EXTRA: \title[On the Impact of Router Virtualization]{On the Impact of Router Virtualization in Content-Centric Networking}
+#+BEAMER_HEADER_EXTRA: \author[K. Tsukamoto]{Keiichiro Tsukamoto\inst{1} and Hiroyuki Ohsaki\inst{1}}
+#+BEAMER_HEADER_EXTRA: \institute{\inst{1} Osaka University, Japan}
+#+BEAMER_HEADER_EXTRA: \date{January 11, 2012}
+#+BEAMER_HEADER_EXTRA: \setlength{\parskip}{1.5ex}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\textbf}{\alert}
+
+* Introduction
+
+** Content-Centric Networking (CCN)
+
+   A data-centric network architecture based on named content
+   - A unique *content identifier* is given to every content
+   - CCN router performs *name-based routing* with longest prefix matching
+   - CCN router has a *buffer cache* for storing forwarded contents
+
+** Virtual Content-Centric Networking (VCCN)
+
+   An extension to CCN, which enables *group-based communication*
+   - *A group identifier* is embedded in the content identifier
+   - CCN router is *virtualized* as multiple instances of VCCN routers
+   - Several VCCN router instances are *logically connected* over CCN network
+
+** Router Virtualization in VCCN
+
+   Several CCN router *resources* are shared among VCCN router instances
+   - ContentStore
+   - FIB (Forward Information Base)
+   - PIT (Pending Information Table)
+
+   Appropriate allocation of CCN router resources to VCCN router
+   instances are crucial in terms of efficiency, fairness,
+   scalability, and security
+
+** (Possible) Positive and Negative Impacts of Router Virtualization
+
+   - *Positive impact*
+     - Router resource allocation to VCCN router instances *increases
+       locality of resource accesses*, which should lead to more
+       efficient resource usage
+
+   - *Negative impact*
+     - Router resource allocation to VCCN router instances *prevents
+       statistical multiplexing effect*, which should lead to less
+       efficient resource usage
+
+** Motivation
+
+   Research interest:
+   - How does the router virtualization in VCCN affect the performance
+     of VCCN?
+
+** Objectives
+
+   We evaluate the performance of VCCN (i.e., CCN with router
+   virtualization) under several types of *router resource (in
+   particular, ContentStore) allocation methods*, and try to answer
+   the following questions.
+
+   Research questions: 
+   - How is *the overall performance* (i.e., throughput, latency) of
+     VCCNs affected by router virtualization?
+   - How is *the individual performance* (i.e., throughput, latency)
+     of VCCN affected by router virtualization?
+   - How is *the fairness among VCCNs* affected by router
+     virtualization?
+   - For a given scenario, how should *router resources be allocated*
+     to VCCN router instances?
+
+* Related Works
+
+** Related Works
+
+   Tortelli et al.
+   - Tortelli11:Fairness
+   Psaras et al.
+   - Psaras11:Modelling
+   Carofiglio et al.
+   - Carofiglio11:Experimental
+   - Carofiglio11:Modeling
+   - Carofiglio11:Bandwidth
+
+   中身書いてください。
+
+* Simulation
+
+** Experiment Setup (1/5)
+
+   - Network topology
+     - aggregation network topology (binary tree network)
+     - core network topology (Abilene network)
+     - hybrid network topology (scale-free network?)
+     サーバがどこにある?
+
+   - Network parameters
+     - Link capacity: 10 [Gbit/s]
+     - Propagation delay: 10 [ms]
+
+** Experiment Setup: Aggregation Network Topology (2/5)
+
+** Experiment Setup: Core Network Topology (3/5)
+
+** Experiment Setup: Hybrid Network Topology (4/5)
+
+** Experiment Setup (5/5)
+
+   - Contents
+     - Number of contents: XXX
+     - Content size distribution: XXX
+
+   - Routers
+     - ContentStore size: XXXX - XXX 
+     - Cache replacement policy: LRU
+
+   - Workload
+     - Number of groups: XXX
+     - Number of users in a group: XXX
+     - Content request rate per user: XXX
+
+** Resource Allocation Methods
+
+   - Shared
+     - ContentStore is shared by all VCCN router instances
+   - Partially-Shared
+     - A fraction of ContentStore is shared by all VCCN router
+       instances, and the rest is equally divided and assigned to
+       every VCCN router instance
+   - Seperated
+     - ContentStore is equally divided and assigned to every VCCN
+       router instance
+
+** Metrics
+
+   - Throughput (mean and CV (coefficient of variation))
+   - Fairness index
+     式を書く
+   - Content delivery delay (mean and CV (coefficient of variation))
+   - Link utilization (average and maximum)
+
+** Simulation Result: The size of assigned ContentStore v.s. Efficiency
+ここ、上にあわせて再考して埋めてください
+予想グラフ (手書で、X、Y軸、線、数字、ラベルが入ったもの) を入れてください
+
+** Simulation Result: The effect of impact of a group in a given CCN network
+ここ、上にあわせて再考して埋めてください
+予想グラフ (手書で、X、Y軸、線、数字、ラベルが入ったもの) を入れてください
+
+必要に応じてスライド数増やしてください。
+
+* Conclusion
+
+上にあわせて埋めてください。

Makefile

@@ -0,0 +1,15 @@
+all:	
+	platex paper.tex
+	bibtex paper
+	platex paper.tex
+	platex paper.tex
+	dvipdfmx paper.dvi
+
+part:
+	platex paper.tex
+	dvipdfmx paper.dvi
+
+push:
+	git add .
+	git commit -am 'update'
+	git push

beamerthemeOhsaki.sty

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+% All rights reserved.
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beamerthemeOhsaki.sty~

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+% All rights reserved.
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bib/quantum.bib

@@ -0,0 +1,9 @@
+@inproceedings{Liu24:INFOCOM,
+  title     = {{LinkSelFiE: Link Selection and Fidelity Estimation in Quantum Networks}},
+  author    = {Liu, Maoli and Li, Zhuohua and Wang, Xuchuang and Lui, John C.S.},
+  booktitle = {Proceedings of the 43rd IEEE Conference on Computer
+                  Communications (INFOCOM 2024)},
+  pages     = {1421--1430},
+  year      = {2024},
+  month     = may,
+}

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+% End plot #6
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+end
+showpage
+%%Trailer
+%%DocumentFonts: Helvetica

ieicejsp.cls

@@ -0,0 +1,796 @@
+\NeedsTeXFormat{pLaTeX2e}
+\ProvidesClass{ieicejsp}
+\newcounter{@paper}
+\def\affliate#1{\gdef\@affliate{#1}}
+\newif\if@landscape \@landscapefalse
+\newcommand{\@ptsize}{}
+\newif\if@restonecol
+\hour\time \divide\hour by 60\relax
+\@tempcnta\hour \multiply\@tempcnta 60\relax
+\minute\time \advance\minute-\@tempcnta
+\newif\if@stysize \@stysizefalse
+\newif\if@enablejfam \@enablejfamtrue
+\DeclareOption{a4paper}{\setcounter{@paper}{1}%
+  \setlength\paperheight {297mm}%
+  \setlength\paperwidth  {210mm}}
+\DeclareOption{a4j}{\setcounter{@paper}{1}\@stysizetrue
+  \setlength\paperheight {297mm}%
+  \setlength\paperwidth  {210mm}}
+\DeclareOption{a4p}{\setcounter{@paper}{1}\@stysizetrue
+  \setlength\paperheight {297mm}%
+  \setlength\paperwidth  {210mm}}
+\DeclareOption{10pt}{\renewcommand{\@ptsize}{0}}
+\DeclareOption{landscape}{\@landscapetrue
+  \setlength\@tempdima{\paperheight}%
+  \setlength\paperheight{\paperwidth}%
+  \setlength\paperwidth{\@tempdima}}
+\DeclareOption{tombow}{%
+  \tombowtrue \tombowdatetrue
+  \setlength{\@tombowwidth}{.1\p@}%
+  \@bannertoken{%
+     \jobname\space:\space\number\year/\number\month/\number\day
+      (\number\hour:\number\minute)}
+  \maketombowbox}
+\DeclareOption{tombo}{%
+  \tombowtrue \tombowdatefalse
+  \setlength{\@tombowwidth}{.1\p@}%
+  \maketombowbox}
+\DeclareOption{mentuke}{%
+  \tombowtrue \tombowdatefalse
+  \setlength{\@tombowwidth}{\z@}%
+  \maketombowbox}
+\DeclareOption{oneside}{\@twosidefalse}
+\DeclareOption{twoside}{\@twosidetrue}
+\DeclareOption{onecolumn}{\@twocolumnfalse}
+\DeclareOption{twocolumn}{\@twocolumntrue}
+\DeclareOption{leqno}{\input{leqno.clo}}
+\DeclareOption{fleqn}{\input{fleqn.clo}}
+\DeclareOption{openbib}{%
+  \AtEndOfPackage{%
+   \renewcommand\@openbib@code{%
+      \advance\leftmargin\bibindent
+      \itemindent -\bibindent
+      \listparindent \itemindent
+      \parsep \z@
+      }%
+   \renewcommand\newblock{\par}}}
+\if@compatibility
+\else
+  \DeclareOption{disablejfam}{\@enablejfamfalse}
+\fi
+\DeclareOption{draft}{\setlength\overfullrule{5pt}}
+\DeclareOption{final}{\setlength\overfullrule{0pt}}
+\ExecuteOptions{a4paper,10pt,oneside,onecolumn,final}
+\ProcessOptions\relax
+%%
+\renewcommand{\normalsize}{%
+    \@setfontsize\normalsize\@xpt{12.9}%
+  \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
+  \abovedisplayshortskip \z@ \@plus3\p@
+  \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
+   \let\@listi\@listI}
+\normalsize
+\setbox0\hbox{\char\euc"A1A1}%
+\setlength\Cht{\ht0}
+\setlength\Cdp{\dp0}
+\setlength\Cwd{\wd0}
+\setlength\Cvs{\baselineskip}
+\setlength\Chs{\wd0}
+\newcommand{\small}{%
+  \@setfontsize\small\@ixpt{11}%
+  \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
+  \abovedisplayshortskip \z@ \@plus2\p@
+  \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
+  \def\@listi{\leftmargin\leftmargini
+              \topsep 4\p@ \@plus2\p@ \@minus2\p@
+              \parsep 2\p@ \@plus\p@ \@minus\p@
+              \itemsep \parsep}%
+  \belowdisplayskip \abovedisplayskip}
+\newcommand{\footnotesize}{%
+  \@setfontsize\footnotesize\@viiipt{9.5}%
+  \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
+  \abovedisplayshortskip \z@ \@plus\p@
+  \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
+  \def\@listi{\leftmargin\leftmargini
+              \topsep 3\p@ \@plus\p@ \@minus\p@
+              \parsep 2\p@ \@plus\p@ \@minus\p@
+              \itemsep \parsep}%
+  \belowdisplayskip \abovedisplayskip}
+\newcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt}
+\newcommand{\tiny}{\@setfontsize\tiny\@vpt\@vipt}
+\newcommand{\large}{\@setfontsize\large\@xiipt{17}}
+\newcommand{\Large}{\@setfontsize\Large\@xivpt{21}}
+\newcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{25}}
+\newcommand{\huge}{\@setfontsize\huge\@xxpt{28}}
+\newcommand{\Huge}{\@setfontsize\Huge\@xxvpt{33}}
+\setlength\topskip{1\Cht}
+\setlength\footskip{30\p@}
+\if@compatibility
+  \setlength\maxdepth{4\p@}
+\else
+  \setlength\maxdepth{.5\topskip}
+\fi
+\setlength\textwidth{\paperwidth}
+\setlength\oddsidemargin{18.1mm}
+\setlength\evensidemargin{18.1mm}
+\setlength\columnsep{7.1mm}
+\addtolength\textwidth{-\oddsidemargin}
+\addtolength\textwidth{-\evensidemargin}
+\addtolength\oddsidemargin{-1in}
+\addtolength\evensidemargin{-1in}
+\@settopoint\textwidth
+\@settopoint\oddsidemargin
+\@settopoint\evensidemargin
+\@settopoint\columnsep
+   \if@twoside
+     \setlength\marginparwidth{.6\@tempdima}
+     \addtolength\marginparwidth{-.4in}
+   \else
+     \setlength\marginparwidth{.5\@tempdima}
+     \addtolength\marginparwidth{-.4in}
+   \fi
+   \ifdim \marginparwidth >2in
+     \setlength\marginparwidth{2in}
+   \fi
+   \@settopoint\marginparwidth
+\setlength\topmargin{30mm}
+\addtolength\topmargin{-1in}
+\setlength\headheight{0\p@}
+\setlength\headsep{0\p@}
+\setlength\textheight{\paperheight}
+\addtolength\textheight{-\topmargin}
+\addtolength\textheight{-\headheight}
+\addtolength\textheight{-\headsep}
+\addtolength\textheight{-27mm}
+\addtolength\textheight{-1in}
+\if@twocolumn
+  \setlength\marginparsep{10\p@}
+\else
+  \setlength\marginparsep{10\p@}
+\fi
+\setlength\marginparpush{5\p@}
+\setlength\footnotesep{6.65\p@}
+\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep    {3\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\textfloatsep{10\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep   {6\p@ \@minus 2\p@}
+\setlength\dblfloatsep    {3\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dbltextfloatsep{5\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@ \@plus 1fil}
+\setlength\@fpsep{4\p@ \@plus 2fil}
+\setlength\@fpbot{0\p@ \@plus 1fil}
+\setlength\@dblfptop{0\p@ \@plus 1fil}
+\setlength\@dblfpsep{4\p@ \@plus 2fil}
+\setlength\@dblfpbot{0\p@ \@plus 1fil}
+\setlength\partopsep{1\p@ \@plus 1\p@ \@minus 1\p@}
+\def\@listi{\leftmargin\leftmargini
+  \parsep 2\p@ \@plus1\p@ \@minus\p@
+  \topsep 2\p@ \@plus1\p@ \@minus2\p@
+  \itemsep2\p@ \@plus1\p@ \@minus\p@}
+\let\@listI\@listi
+\@listi
+\def\@listii{\leftmargin\leftmarginii
+   \labelwidth\leftmarginii \advance\labelwidth-\labelsep
+   \topsep  2\p@ \@plus2\p@ \@minus\p@
+   \parsep  1\p@ \@plus\p@  \@minus\p@
+   \itemsep\parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+   \labelwidth\leftmarginiii \advance\labelwidth-\labelsep
+   \topsep\z@
+   \parsep\z@
+   \partopsep \p@ \@plus\z@ \@minus\p@
+   \itemsep\topsep}
+%%
+\def\@listiv {\leftmargin\leftmarginiv
+              \labelwidth\leftmarginiv
+              \advance\labelwidth-\labelsep}
+\def\@listv  {\leftmargin\leftmarginv
+              \labelwidth\leftmarginv
+              \advance\labelwidth-\labelsep}
+\def\@listvi {\leftmargin\leftmarginvi
+              \labelwidth\leftmarginvi
+              \advance\labelwidth-\labelsep}
+%%
+\setlength\columnsep{7mm}
+\setlength\columnseprule{0\p@}
+\setlength\lineskip{1\p@}
+\setlength\normallineskip{1\p@}
+\renewcommand{\baselinestretch}{}
+\setlength\parskip{0\p@ \@plus \p@}
+\setlength\parindent{1\Cwd}
+\@lowpenalty   51
+\@medpenalty  151
+\@highpenalty 301
+\setcounter{topnumber}{2}
+\setcounter{bottomnumber}{1}
+\setcounter{totalnumber}{3}
+\setcounter{dbltopnumber}{2}
+\renewcommand{\topfraction}{.7}
+\renewcommand{\bottomfraction}{.3}
+\renewcommand{\textfraction}{.2}
+\renewcommand{\floatpagefraction}{.5}
+\renewcommand{\dbltopfraction}{.7}
+\renewcommand{\dblfloatpagefraction}{.5}
+\def\ps@plain{\let\@mkboth\@gobbletwo
+   \let\ps@jpl@in\ps@plain
+   \let\@oddhead\@empty
+   \def\@oddfoot{\reset@font\hfil\thepage\hfil}%
+   \let\@evenhead\@empty
+   \let\@evenfoot\@oddfoot}
+\let\ps@jpl@in\ps@plain
+\def\ps@headnombre{\let\@mkboth\@gobbletwo
+    \let\ps@jpl@in\ps@headnombre
+  \def\@evenhead{\thepage\hfil}%
+  \def\@oddhead{\hfil\thepage}%
+  \let\@oddfoot\@empty\let\@evenfoot\@empty}
+\def\ps@footnombre{\let\@mkboth\@gobbletwo
+    \let\ps@jpl@in\ps@footnombre
+  \def\@evenfoot{\thepage\hfil}%
+  \def\@oddfoot{\hfil\thepage}%
+  \let\@oddhead\@empty\let\@evenhead\@empty}
+\if@twoside
+  \def\ps@headings{\let\ps@jpl@in\ps@headnombre
+    \let\@oddfoot\@empty\let\@evenfoot\@empty
+    \def\@evenhead{\thepage\hfil\leftmark}%
+    \def\@oddhead{{\rightmark}\hfil\thepage}%
+    \let\@mkboth\markboth
+    \def\sectionmark##1{\markboth{%
+       \ifnum \c@secnumdepth >\z@ \thesection.\hskip1zw\fi
+       ##1}{}}%
+    \def\subsectionmark##1{\markright{%
+       \ifnum \c@secnumdepth >\@ne \thesubsection.\hskip1zw\fi
+       ##1}}%
+  }
+\else % if not twoside
+  \def\ps@headings{\let\ps@jpl@in\ps@headnombre
+    \let\@oddfoot\@empty
+    \def\@oddhead{{\rightmark}\hfil\thepage}%
+    \let\@mkboth\markboth
+  \def\sectionmark##1{\markright{%
+     \ifnum \c@secnumdepth >\m@ne \thesection.\hskip1zw\fi
+     ##1}}%
+  }
+\fi
+\if@twoside
+  \def\ps@bothstyle{\let\ps@jpl@in\ps@footnombre
+    \def\@evenhead{\leftmark\hfil}% right page
+    \def\@evenfoot{\thepage\hfil}% right page
+    \def\@oddhead{\hfil\rightmark}% left page
+    \def\@oddfoot{\hfil\thepage}% left page
+  \let\@mkboth\markboth
+  \def\sectionmark##1{\markboth{%
+     \ifnum \c@secnumdepth >\z@ \thesection.\hskip1zw\fi
+     ##1}{}}%
+  \def\subsectionmark##1{\markright{%
+     \ifnum \c@secnumdepth >\@ne \thesubsection.\hskip1zw\fi
+     ##1}}%
+  }
+\else % if one column
+  \def\ps@bothstyle{\let\ps@jpl@in\ps@footnombre
+    \def\@oddhead{\hfil\rightmark}%
+    \def\@oddfoot{\hfil\thepage}%
+    \let\@mkboth\markboth
+  \def\sectionmark##1{\markright{%
+     \ifnum \c@secnumdepth >\m@ne \thesection.\hskip1zw\fi
+     ##1}}%
+  }
+\fi
+\def\ps@myheadings{\let\ps@jpl@in\ps@plain%
+  \let\@oddfoot\@empty\let\@evenfoot\@empty
+  \def\@evenhead{\thepage\hfil\leftmark}%
+  \def\@oddhead{{\rightmark}\hfil\thepage}%
+  \let\@mkboth\@gobbletwo
+  \let\sectionmark\@gobble
+  \let\subsectionmark\@gobble
+}
+\def\p@thanks#1{\footnotemark
+  \protected@xdef\@thanks{\@thanks
+    \protect{\noindent$\m@th^\thefootnote$~#1\protect\par}}}
+  \newcommand{\maketitle}{\par
+  \begingroup
+    \parskip 0em
+    \renewcommand{\thefootnote}{\fnsymbol{footnote}}%
+    \def\@makefnmark{\hbox{\ifydir $\m@th^{\@thefnmark}$
+      \else\hbox{\yoko$\m@th^{\@thefnmark}$}\fi}}%
+     \long\def\@makefntext##1{\parindent 1em\noindent
+       \hbox to1.8em{\hss$\m@th^{\@thefnmark}$}##1}%
+    \if@twocolumn
+      \ifnum \col@number=\@ne \@maketitle
+      \else \twocolumn[\@maketitle]%
+      \fi
+    \else
+      \newpage
+      \global\@topnum\z@   % Prevents figures from going at top of page.
+      \@maketitle
+    \fi
+    \thispagestyle{empty}\@thanks
+  \endgroup
+  \setcounter{footnote}{0}%
+  \global\let\thanks\relax
+  \global\let\maketitle\relax
+  \global\let\p@thanks\relax
+  \global\let\@thanks\@empty
+  \global\let\@author\@empty
+%%
+  \global\let\@affliate\@empty
+%%
+  \global\let\@date\@empty
+  \global\let\@title\@empty
+  \global\let\title\relax
+  \global\let\author\relax
+%%
+  \global\let\affliate\relax
+%%
+  \global\let\date\relax
+  \global\let\and\relax
+  }
+  \def\@maketitle{%
+  \newpage\null
+  \begin{center}%
+  \let\footnote\thanks
+    {\LARGE \baselineskip 15pt \@title \par}%
+    \vskip 1.0em%
+    {
+      \lineskip .0em%
+      \begin{tabular}[t]{c}%
+      \baselineskip 0em%
+        \@author
+      \end{tabular}\par}%
+    \vskip 1em%
+    {\small
+      \lineskip .0em%
+      \begin{tabular}[t]{c}%
+      \baselineskip 0em%
+        \@affliate
+      \end{tabular}\par}%
+    \vskip 1em%
+  \end{center}%
+    \vskip 0.5em}%
+  \newenvironment{abstract}{%
+    \if@twocolumn
+      \section*{\abstractname}%
+    \else
+      \small
+      \begin{center}%
+        {\bfseries\abstractname\vspace{-.5em}\vspace{\z@}}%
+      \end{center}%
+      \quotation
+    \fi}{\if@twocolumn\else\endquotation\fi}
+\setcounter{secnumdepth}{3}
+\newcounter{part}
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paper.aux

@@ -0,0 +1,12 @@
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+\citation{Liu24:INFOCOM}
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+\@writefile{toc}{\contentsline {section}{\numberline {3}提案手法 : 二段階貪欲法(Two-Phase Greedy)による資源配分}{2}}
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+\gdef \@abspage@last{2}

paper.bbl

@@ -0,0 +1,9 @@
+\begin{thebibliography}{1}
+
+\bibitem{Liu24:INFOCOM}
+M.~Liu, Z.~Li, X.~Wang, and J.~C. Lui, ``{LinkSelFiE: Link Selection and
+  Fidelity Estimation in Quantum Networks},'' in {\em Proceedings of the 43rd
+  IEEE Conference on Computer Communications (INFOCOM 2024)}, pp.~1421--1430,
+  May 2024.
+
+\end{thebibliography}

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paper.tex

@@ -0,0 +1,408 @@
+% -*- japanese-LaTeX -*-
+% 
+% 
+% Copyright (c) 2016, Hiroyuki Ohsaki.
+% All rights reserved.
+% 
+% $Id: paper.tex,v 1.4 2020/08/27 16:31:45 ohsaki Exp ohsaki $
+% 
+
+\documentclass[twocolumn,dvipdfmx, a4paper]{ieicejsp}
+\usepackage{cite} \usepackage{insertfig} \usepackage{times}
+\usepackage{url} \usepackage{revhistory} \usepackage{amsmath}
+\usepackage{float} \usepackage{comment} \usepackage{algorithm,
+  algpseudocode}
+
+
+%% \importrevisions
+
+\makeatletter \renewcommand{\thesection}{\@arabic\c@section}
+\renewcommand{\thesubsection}{\thesection.\,\@arabic\c@subsection}
+\renewcommand{\ext@subfigure}{lof} \renewcommand{\baselinestretch}{.6}
+\makeatother
+
+
+
+\title{{\bf 通信需要を考慮した量子ネットワークの\\リンク忠実度計測手法
+    に関する一検討}\\ {\normalsize  A Study on Link Fidelity Measurement in Quantum Networks Considering Communication Demand }}
+
+\author{
+  山近 駿   $^1$ \\ Shun Yamachika \and
+  柿原 悠人 $^2$ \\ Yuto Kakihara \and
+  井上 翔太 $^2$ \\ Shota Inoue \and
+  大崎 博之 $^2$ \\ Hiroyuki Ohsaki
+}
+
+
+\affliate{
+  関西学院大学 工学部 情報工学課程 $^1$ \\
+  Department of Computer Science, School of Engineering, Kwansei Gakuin University \\  
+  関西学院大学 大学院理工学部研究科 情報工学専攻 $^2$ \\
+  Department of Informatics, Graduate School of Science and
+  Technology, Kwansei Gakuin University \\
+}%% fixme: 所属が正しいか確認しておいてください。 -shota
+
+
+
+\renewcommand{\baselinestretch}{0.005}
+
+
+\begin{document}
+\setlength{\parskip}{0.2pt}  % 段落間の余白をゼロにする
+
+\maketitle
+
+
+\section{はじめに}
+
+%% ### トピックセンテンス
+
+%% 1.  次世代の情報通信基盤として期待される量子ネットワークの研究開発
+%% が世界的に加速している。
+
+%% 2.  量子ネットワーク上で高信頼な通信を実現するためには、環境ノイズ
+%% の影響を受けにくい、すなわち忠実度の高い量子リンクを選択することが
+%% 不可欠である。
+
+%% 3.  しかし、各リンクの忠実度を正確に推定するには多数回の量子測定が
+%% 必要であり、ネットワーク全体の性能を維持するためには、限られた測定
+%% 資源をいかに効率的に配分するかが極めて重要な課題となる。
+
+%% 4.  この測定資源配分問題に対する有力なアプローチとして、複数リンク
+%% の中から最も忠実度の高い一本を効率的に特定する手法「LinkSelFiE」が
+%% 提案されている。
+
+%% 5.  LinkSelFiEは、すべてのリンク候補を等価な存在として扱う問題設定
+%% において、測定コストを大幅に削減する優れた手法であるが、実用的なネッ
+%% トワーク運用では、各通信経路の重要度（通信需要）は一様ではない。
+
+%% 6.  例えば、重要な機密情報を扱う通信経路や、高いサービス品質保証
+%% (QoS) が求められる経路は、そうでない経路に比べて、その品質を保証す
+%% ることの価値が本質的に高い。
+
+%% 7.  したがって、ネットワーク全体の運用価値を最大化するためには、各
+%% 通信経路の重要度を考慮し、価値の高い経路へ優先的に測定資源を配分す
+%% る、新たな資源配分フレームワークが求められる。
+
+%% 8.  そこで本研究では、通信需要を考慮したリンク忠実度計測という新た
+%% な問題を定義し、その解決を目的とする。
+
+%% 9.  具体的には、各通信経路の「価値」をその重要度と推定忠実度の積と
+%% して定量化し、ネットワーク全体の総価値を最大化する最適化問題として
+%% 定式化する。
+
+%% 10. この問題に対する効率的かつ実用的な準最適解法として、広域的な探
+%% 索と集中的な活用を組み合わせた「二段階貪欲法 (Two-Phase Greedy
+%% Method)」を提案する。
+
+%% 11. 本稿の貢献は、通信需要という新たな評価軸を導入した問題設定の提
+%% 案、およびその有効な解法の提示にあり、シミュレーション評価を通じて、
+%% 提案手法が既存手法に比べてネットワーク全体の総価値を大幅に向上させ
+%% ることを定量的に示す。
+
+
+近年、量子コンピュータや量子通信といった量子技術の研究開発が世界的に加
+速している。中でも、量子ビットを情報媒体として遠隔地間で伝送・共有する
+量子ネットワークは、盗聴不可能な量子鍵配送 (QKD) や、分散量子コンピュー
+ティング、高精度な量子センシング網を実現する次世代の情報通信基盤として
+大きな期待が寄せられている。量子ネットワークの究極的な目標は、地球規模
+での高忠実度な量子状態の共有、すなわち量子インターネットの実現にある。
+
+しかし、その実現に向けた道のりには数多くの技術的課題が存在する。最も根
+源的な課題の一つが、量子情報の担い手である量子ビットの脆弱性である。量
+子ビットは、光ファイバ等の伝送媒体や周辺環境との相互作用（環境ノイズ）
+によって、その繊細な量子状態が容易に破壊されてしまうデコヒーレンスと呼
+ばれる現象に常に晒されている。この状態の劣化は通信品質の低下に直結し、
+忠実度の低いリンク、すなわち入力された量子状態を正確に出力できないリン
+クを用いては、意味のある通信を行うこと自体が困難となる。したがって、量
+子ネットワーク上で高信頼な通信を実現するためには、ネットワーク内に物理
+的に存在する多数のリンクの中から、環境ノイズの影響を受けにくく、忠実度
+の高い量子リンクを効率的に選択することが不可欠である。
+
+
+ここで重要となるのが、各リンクの忠実度をいかにして知るかという問題であ
+る。リンクの忠実度は、プロトタイプの量子もつれ光子源の性能揺らぎや、敷
+設された光ファイバの温度変化といった動的な要因によって時間的に変動しう
+るため、ネットワークを運用する上で定期的な計測と推定が不可欠となる。し
+かし、この忠実度を統計的に十分な精度で推定するには、対象リンクを用いて
+多数回にわたる量子状態の生成、伝送、そして測定を繰り返す必要がある。
+
+この一連のプロセスは、ネットワークの貴重な資源、すなわち測定時間や量子
+ビットそのものを大量に消費する。測定に費やされる資源は、本来のデータ通
+信に利用できないため、過度な測定はネットワーク全体の通信スループットを
+著しく低下させる。ここに、忠実度推定の精度とコストの間に存在する根本的
+なトレードオフが生じる。この制約の下で、限られた測定資源をネットワーク
+上のどのリンクに、どれだけ配分するかを決定する測定資源配分は、量子ネッ
+トワークの実用化に向けた極めて重要な最適化問題となる。
+
+
+この測定資源配分問題に対する有力なアプローチとして、Liuらによって提案
+されたLinkSelFiEが存在する \cite{Liu24:INFOCOM}。LinkSelFiEは、強化学
+習における多腕バンディット問題の知見を応用し、複数の並列リンクの中から
+最も忠実度の高い一本を特定する際に、有望なリンクの測定回数を動的に増や
+し、そうでないリンクの測定を早期に打ち切ることで、総測定コストを大幅に
+削減しつつ高い特定精度を実現する。これは、同一ノードペア間に複数の物理
+リンクが存在する状況において、最良のリンクを効率的に見つけ出すという問
+題設定に対する、非常に洗練された解法である。
+
+LinkSelFiEは、すべてのリンク候補を等価な存在として扱い、その中から純粋
+に最も物理的な品質が高いリンクを探し出すことに特化している。しかし、よ
+り広域で多様なアプリケーションが動作する実用的なネットワーク運用の観点
+からは、異なる課題が見えてくる。実際のネットワークでは、各通信経路の重
+要度（通信需要）は一様ではない。例えば、国家の安全保障に関わる量子暗号
+通信に用いられる経路と、基礎科学実験のための低優先度なデータ転送に用い
+られる経路とでは、その通信品質を保証することの価値が本質的に異なる。前
+者の品質がわずかに低下することは許容しがたい一方、後者であれば多少の品
+質劣化は許容できるかもしれない。
+
+このように、アプリケーションの要求やサービスレベル合意 (SLA) に応じて、
+各通信経路には異なる重要度が設定されるのが自然である。このような状況に
+おいて、すべてのリンクを等価に扱う従来のアプローチでは、重要度の低い経
+路の忠実度を高精度に推定するために貴重な測定資源を費やす一方で、本当に
+重要な経路の品質保証が疎かになるという、ネットワーク全体の運用価値を損
+なう非効率な資源配分を招きかねない。したがって、ネットワーク全体の運用
+価値を最大化するためには、各通信経路の重要度を定量的な指標として導入し、
+価値の高い経路へ優先的に測定資源を配分する、新たな資源配分フレームワー
+クが求められる。
+
+
+そこで本研究では、通信需要を考慮したリンク忠実度計測という新たな問題を
+定義し、その解決を目的とする。我々は、各通信経路の価値を、その経路が担
+う通信の重要度と、経路内で最も忠実度の高いリンクの推定忠実度の積として
+定量化する。この定義に基づき、本研究が取り組む問題を与えられた総測定予
+算の制約下で、ネットワーク全体の総価値を最大化する測定資源配分を決定す
+る最適化問題として定式化する。
+
+この問題は、どのノードペア（通信経路）に資源を配分し、さらにその中でど
+のリンクを測定するかという組合せ最適化問題であり、厳密解を求めることは
+計算論的に極めて困難である。そのため、本稿ではこの問題に対する効率的か
+つ実用的な準最適解法として、**二段階貪欲法 (Two-Phase Greedy Method)**
+を提案する。本手法は、第一段階（広域探索フェーズ）で、ごく少量の測定資
+源を全リンクに広く薄く配分して忠実度の初期推定値を得る。続く第二段階
+（活用フェーズ?）では、第一段階で得られた初期推定忠実度と各経路の重要度
+から算出される価値スコアに基づき、最も価値創出が期待される有望な経路群
+に残りの測定資源を集中的に投下する。この戦略により、計算コストを低く抑
+えつつ、準最適な資源配分を実現する。
+
+
+本研究の貢献は以下のとおりである。
+\begin{itemize}
+
+\item 従来の物理的なリンク品質の推定問題を発展させ、通信需要という経済
+  的・運用的な価値尺度を導入した、より実践的なネットワーク総価値最大化
+  問題を初めて定式化した。
+  
+\item 上記の問題に対する効率的な近似解法として、二段階貪欲法を提案した。
+  これは、探索と活用を明確に分離することで、大規模ネットワークにおいて
+  も実用的な計算時間で高品質な解を得ることを可能にする。
+  
+\item 量子ネットワークシミュレータを用いた評価実験を通じて、提案手法が、
+  通信需要を考慮しない既存のアプローチに比べて、ネットワーク全体の総価
+  値を大幅に向上させることを定量的に明らかにした。
+  
+\end {itemize}  
+
+本稿の構成は以下の通りである。2章で本研究が対象とする問題モデルと目的
+関数を定義する。3章では提案手法である二段階貪欲法の詳細を述べる。4章で
+シミュレーション評価の結果を示し、提案手法の有効性を考察する。最後に5
+章で結論と今後の課題を述べる。
+
+
+\section{通信需要を考慮したリンク忠実度計測問題}
+
+%% 本問題は通信需要の大きさが異なる複数ノードペアに対し最適な測定資源配分
+%% を決定する問題として定式化される。これは単一ノードペア間の最高忠実度リ
+%% ンク特定問題を、より現実的な状況へ拡張したものである。
+
+%% 本問題の入力はネットワーク構成と総測定予算である。具体的には単一の対象
+%% ノード $S$ と $N$ 個の隣接ノード集合、各ノードペア $(S, D_n)$ 間の並列
+%% リンク集合 $L_n$、各ノードペアの重要度 $I_n$、そして総測定予算 $C$ が
+%% 与えられる。ただし、各リンク $l_{nj}$ の真の忠実度 $f_{nj}$ は未知であ
+%% る。
+
+%% 問題の出力は測定予算内で選択された価値ある通信経路の集合である。アルゴ
+%% リズムは価値が高いと判断した $K$ 個のノードペア集合 $S_{sel}$ を決定す
+%% る。そして選択された各ノードペア $n_k$ において最も忠実度が高いと特定
+%% されたリンク $l_{nk}^*$ とその推定忠実度 $\hat{F}^*_{nk}$ を出力する。
+
+%% 本問題の目的は目的関数 ($\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}$)
+%% で定義されるネットワーク全体の総価値を最大化することである。これは選択
+%% された全経路の価値すなわち重要度と忠実度の積の総和を示す。
+
+%% \radd{このとき、制約条件は、全リンクにおける総測定コストが総測定予算
+%%   $C$ を超えないこと、すなわち 
+%%   $\sum^N_{n=1} \sum_{l \in L_n}  Cost(l) \leq C$
+%%   で与えられる。
+%% }
+
+本問題は、通信需要 (重要度 $I_n$) が異なる $N$ 個のノードペア$(S,
+D_n)$に対し、総測定予算 $C$ の制約下で、ネットワーク全体の総価値を最大
+化する測定資源配分を決定する問題である。各ノードペアは並列リン
+ク集合 $L_n$ を持ち、各リンク $l_{nj}$ の真の忠実度$f_{nj}$ は未知とす
+る。
+
+本問題は、価値が高いと判断したノードペア集合 $S_{sel}$ 選択し、
+各ペア $n_k \in S_{sel}$ で最高と推定されたリンク忠実度$F^*_{nk}$ を用
+いて、以下の目的関数で定義される総価値を最大化することである。
+{\footnotesize
+  \begin{align}
+    \text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}
+  \end{align}
+}
+
+このとき、制約条件は、全リンクにおける総測定コストが総測定予算$C$ を超
+えないこと、すなわち $\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C$で
+与えられる。
+
+
+\section{提案手法 : 二段階貪欲法(Two-Phase Greedy)による資源配分}
+
+%% 本稿では上記の問題を解くためにTwo-Phase Greedy手法を提案する。本手法は
+%% 広域的な探索と集中的な活用の二段階処理により限られた測定資源を効率的に
+%% 配分する。第一段階では全リンクに対して少量の測定を行い忠実度の初期推定
+%% 値を低コストで得る。これによりネットワーク全体の品質分布を大局的に把握
+%% する。
+
+%% 第二段階では第一段階の結果を基に残りの測定資源を価値が高いと見込まれる
+%% 有望なリンクへ集中的に投下する。具体的には各ノードペアの重要度 $I_n$
+%% と初期推定忠実度 $\hat{f}_n$ の積から価値スコアを計算する。そして価値
+%% の高いノードペア内のリンク群にのみLinkSelFiEを適用し詳細な測定を行う。
+%% この貪欲戦略により測定資源は価値創出の期待値が高い経路の特定へ自動的に
+%% 集中し総価値の効率的な最大化が期待できる。
+
+本稿では、上記の問題を解くための効率的な近似解法として、広域的な探索と
+集中的な活用を組み合わせた二段階貪欲法を提案する。この手法は、
+組合せ最適化問題に対する現実的なアプローチとして、限られた測定資源を準
+最適に配分し、計算コストを抑えつつ高い性能を実現することを目的とする。
+
+二段階貪欲法の第一段階は、広域探索フェーズである。ここでは、限ら
+れた測定予算の一部を、対象となる全てのリンクに少量ずつ均等に配分するこ
+とで、各リンクの忠実度の初期推定値を低コストで得る。
+
+本手法の第二段階は、活用フェーズである。ここでは、広域探索フェーズで得
+られた初期推定忠実度と各ノードペアの重要度の積から価値スコアを算出し、
+このスコアが高い有望なノードペア内のリンク群に残りの測定資源を集中的に
+投下する。具体的には、各ノードペア $n$ に対して価値スコア
+$I_n\hat{f}_n$を計算し、スコアの高い順にノードペアを選択する。
+
+%% そして、選
+%% 択されたノードペア内のリンク群に対してのみ、先行研究である LinkSelFiE
+%% を適用し、最も忠実度の高いリンクを高い精度で特定する。
+%% この貪欲戦略により、測定資源は価値創出の期待値が高い経路の特
+%% 定へと自動的に割り当てられ、ネットワーク全体の総価値が効率的に最大化さ
+%% れることが期待できる。
+
+
+\section{実験}
+\begin{figure}[t]
+  \centering
+  \begin{minipage}[b]{0.235\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{graphA.eps}
+    \vspace{0.5em}
+    
+    {\scriptsize 図1: 隣接ノード数3における\\測定予算と総価値スコアの関係}
+    \label{fig:r3}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[b]{0.235\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{graphC.eps}
+    \vspace{0.5em}
+    
+    {\scriptsize 図2: 隣接ノード数5における\\測定予算と総価値スコアの関係}
+    \label{fig:r5}
+  \end{minipage}
+\end{figure}
+
+本章では、提案手法がネットワーク全体の総価値を効率的に最大化できること
+を示すため、量子ネットワークシミュレータ NetSquid を用いた評価実験を行っ
+た。
+
+
+本実験では、1つの対象ノードに接続する隣接ノード数が $N=3$ および $N=5$ の2種類のスター型トポロジを用いた。各ノードペア間には5本のリンクが存在し、そのうち1本の平均忠実度を $0.95$、残りの4本を $0.85$ とする正規分布に従って忠実度を設定した。各ノードペアの重要度 $I_n$ は、区間 $[0, 1]$ の一様乱数により決定した。
+
+
+二段階貪欲法の設定として、広域探索フェーズでは、各リンクに対して
+初期予算($t_0=40$)を割り当て、全リンクを均等に測定し初期推定値を得る。
+活用フェーズでは、価値スコアによって選択されたノードペア内のリンク
+群に対して、LinkSelFiEを適用することで、最も忠実度の高いリンクを特定
+する。
+
+比較手法として、Uniform-LinkSelFiEおよびUniform-Naiveを用いた。前者は、
+LinkSelFiEの枠組みで測定予算を全ペアに均等配分し、リンクが一意に定まれ
+ばそのリンクを、そうでなければ推定忠実度が最大のリンクを選出する手法で
+ある。後者は、予算を全ペア・全リンクに均等配分する手法である。
+
+
+評価指標には、測定予算を変化させた際のネットワーク総価値スコアを用い、
+各測定予算の値について、独立なシュミレーションを 20 回実施し、その平均
+値と 95 \% 信頼区間を算出した。
+
+図1および図2の結果から、提案手法は比較手法よりも高い総価値スコアを達成し、価値の高いリンクへ優先的に資源を配分することが示された。ただし、実験で検証した範囲を超えて予算をさらに増加させた場合には、価値の低いリンクにもコストをかけてしまうため、スコアの上昇率は鈍化し、追加投資による価値の向上は限定的になると考えられる。
+
+
+%% 隣接ノードが 3 つの条件での結果 (図 1) では、
+
+%% 測定予算が少ない初期段階でスコアは急激に上昇し、その後、上昇率は緩やか
+%% になる傾向が見られた。これは、提案手法が価値の高いリンクへ優先的に資源
+%% を配分するため、初期の投資で大きな効果が得られる一方、有望なリンクの特
+%% 定が進むにつれて追加投資による価値の向上が限定的になることを示唆してい
+%% る。この結果は、特に資源制約が厳しい状況において提案手法が有効であるこ
+%% とを示している。
+
+%% また、隣接ノードが 5 つの条件での結果 (図 2) では、利用可能な予算が増
+%% えるにつれ、提案手法と比較手法との性能差がより拡大する結果が得られた。
+
+%% 探索対象となるリンクの総数が増加すると、各リンクに割り当て可能な平均測
+%% 定資源は相対的に減少し、資源配分の効率性がより重要となる。このような厳
+%% しい資源制約下において、通信需要と品質に基づいて資源を的確に配分する提
+%% 案手法の優位性がより際立つためであると考えられる。以上の結果から、提案
+%% 手法は、特に大規模で資源制約の厳しい量子ネットワークにおいて、全体の価
+%% 値を最大化する上で高い有効性を持つことが示された。
+
+
+%% 本章では、通信需要（重要度）と忠実度の両方を考慮した資源配分手法の有効
+%% 性を、シミュレーションによって定量的に評価する。具体的には、限られた測
+%% 定予算のもとで、提案手法がネットワーク全体の総価値スコア（$\sum I_n
+%%   \cdot \hat{f}_n^*$）をどれだけ効率的に最大化できるかを検証する。
+
+%% シミュレーションには、量子ネットワークシミュレータである NetSquid を用
+%% いた。評価対象とするネットワークトポロジは、1つの対象ノードと、それに
+%% 接続する隣接ノードの数が3つ（$N=3$）または5つ（$N=5$）の2種類である。
+%% 各ノードペア $(S, D_n)$ の間には、それぞれ5本の独立な量子リンクが存在
+%% すると仮定する。リンクのノイズモデルにはデポラライジングチャネルを適用
+%% し、リンク忠実度は、平均0.95のリンク1本と平均0.85のリンク4本からなる正
+%% 規分布に従って生成された。
+
+%% また、各ノードペアに割り当てられる重要度 $I_n$ は、通信タスクの優先度
+%% を表すパラメータとして、区間 $[0, 1]$ における一様乱数により設定した。
+%% なお、各評価点について20回の独立なシミュレーション試行を行い、その結果
+%% の95\%信頼区間をグラフ中に縦線で示している。
+
+%% 実験結果より、提案手法はすべての測定予算条件において比較手法よりも高い
+%% 総価値スコアを達成しており、その有効性が確認された。一方で、測定予算の
+%% 増加に伴ってスコアの上昇率は徐々に低下する傾向が見られた。これは、提案
+%% 手法が価値の高いリンクに優先的に測定資源を集中させる戦略を取るため、初
+%% 期段階において効果的な投資が行われる一方で、残されたリンク群には相対的
+%% に低い価値しか見込めないためである。この結果から、提案手法は特にリソー
+%% ス制約が厳しい状況において有効であることが示唆される。
+
+%% 図\ref{fig:r3}および図\ref{fig:r5}は、それぞれ隣接ノードが3つ（$N=3$）
+%% および5つ（$N=5$）の場合における、総価値スコアと測定予算の関係を示して
+%% いる。隣接ノード数を3から5へ増加させた場合の評価では、提案手法と比較手
+%% 法との性能差がより顕著に拡大した。隣接ノード数が増加すると、各ノードペ
+%% アに割り当て可能な平均測定資源は相対的に減少する。このような厳しい資源
+%% 制約下において、需要と品質に基づいて資源を的確に配分する提案手法の優位
+%% 性がより際立ったものと考えられる。以上の実験結果から、提案手法は通信需
+%% 要とリンク品質に基づいて測定資源を効率的に配分することにより、特に資源
+%% 制約が厳しい、あるいはネットワーク規模が大きい状況において、全体の価値
+%% を最大化する上で高い有効性を持つことが示された。
+\vspace{-0.4em}  % ← この行を追加（-0.8em 〜 -1.2em で調整）
+
+\section*{謝辞}
+本研究の一部は JSPS 科研費 24K02936 の助成を受けたものである。
+\vspace{-0.5em} % ← この行を追加
+\renewcommand{\em}{\it} \bibliographystyle{ieeetr}
+\bibliography{bib/quantum}
+\end{document}

paper.tex~

@@ -0,0 +1,288 @@
+% -*- japanese-LaTeX -*-
+% 
+% 
+% Copyright (c) 2016, Hiroyuki Ohsaki.
+% All rights reserved.
+% 
+% $Id: paper.tex,v 1.4 2020/08/27 16:31:45 ohsaki Exp ohsaki $
+% 
+
+\documentclass[twocolumn,dvipdfmx, a4paper]{ieicejsp}
+\usepackage{cite} \usepackage{insertfig} \usepackage{times}
+\usepackage{url} \usepackage{revhistory} \usepackage{amsmath}
+\usepackage{float} \usepackage{comment} \usepackage{algorithm,
+  algpseudocode}
+
+
+%% \importrevisions
+
+\makeatletter \renewcommand{\thesection}{\@arabic\c@section}
+\renewcommand{\thesubsection}{\thesection.\,\@arabic\c@subsection}
+\renewcommand{\ext@subfigure}{lof} \renewcommand{\baselinestretch}{.6}
+\makeatother
+
+
+
+\title{{\bf 通信需要を考慮した量子ネットワークの\\リンク忠実度計測手法
+    に関する一検討}\\ {\normalsize  A Study on Link Fidelity Measurement in Quantum Networks Considering Communication Demand }}
+
+\author{
+  山近 駿   $^1$ \\ Shun Yamachika \and
+  柿原 悠人 $^2$ \\ Yuto Kakihara \and
+  井上 翔太 $^2$ \\ Shota Inoue \and
+  大崎 博之 $^2$ \\ Hiroyuki Ohsaki
+}
+
+
+\affliate{
+  関西学院大学 工学部 情報工学課程 $^1$ \\
+  Department of Computer Science, School of Engineering, Kwansei Gakuin University \\  
+  関西学院大学 大学院理工学部研究科 情報工学専攻 $^2$ \\
+  Department of Informatics, Graduate School of Science and
+  Technology, Kwansei Gakuin University \\
+}%% fixme: 所属が正しいか確認しておいてください。 -shota
+
+
+
+\renewcommand{\baselinestretch}{0.005}
+
+
+\begin{document}
+\setlength{\parskip}{0.2pt}  % 段落間の余白をゼロにする
+
+\maketitle
+
+
+\section{はじめに}
+
+量子ネットワークにおける高信頼通信の実現には、高い忠実度な量子リンクの選
+択が不可欠であるが、その推定には多大な測定コストを要するという課題があ
+る。
+%% 量子情報は環境ノイズに対して極めて脆弱であり、通信の成功確率を向上
+%% させるためには、ネットワーク内に存在する多数の物理リンクの中から、量子
+%% 状態を劣化させにくい、すなわち忠実度の高いリンクを効率的に見つけ出し、
+%% 活用する必要がある。しかし、リンクの忠実度を正確に推定するためには多数
+%% 回の測定が必要となり、限られた測定資ん源（時間や量子ビット）をいかに効率
+%% 的に配分するかが重要な課題となる。
+
+LinkSelFiE\cite{Liu24:INFOCOM}は、測定コストを削減しつつ高忠実度リンクを特定
+する手法だが、各通信経路の重要度 (通信需要) を考慮していないため、通信
+需要に基づいて測定資源を配分できない。
+%% LinkSelFiEは、
+%% 複数のリンクの中から最も忠実度の高い一本を効率的に見つけ出す問題設定に
+%% 特化しており、全てのリンク候補を同等に扱う。しかし、実際のネットワーク
+%% 運用では、アプリケーションの要求などに応じて通信経路ごとに重要度が異な
+%% るため、重要度の低いリンクの忠実度を高精度に推定するよりも、重要度の高
+%% いリンクの品質を優先的に保証する方が、システム全体としての価値は高まる。
+
+
+
+そこで本研究では、通信需要を定量的な重みとして導入し、限られた測定資源
+をリンクの価値に応じて最適に配分する新たな手法を提案する。具体的には、
+各通信経路の重要度と忠実度の積をその経路の価値と定義し、ネットワーク全
+体の総価値を最大化する問題として定式化する。この定式化に基づき、限られ
+た測定資源を準最適に配分する二段階貪欲法を提案する。
+%% この問題に対し、効率的な近似解法を提案し、シミュレーション実験を
+%% 通じてその有効性を定量的に示す。これにより、実用上重要な通信経路に測定
+%% 資源を優先的に配分し、ネットワーク全体の運用効率と性能を向上させること
+%% を目指す。
+
+
+\section{通信需要を考慮したリンク忠実度計測問題}
+
+%% 本問題は通信需要の大きさが異なる複数ノードペアに対し最適な測定資源配分
+%% を決定する問題として定式化される。これは単一ノードペア間の最高忠実度リ
+%% ンク特定問題を、より現実的な状況へ拡張したものである。
+
+%% 本問題の入力はネットワーク構成と総測定予算である。具体的には単一の対象
+%% ノード $S$ と $N$ 個の隣接ノード集合、各ノードペア $(S, D_n)$ 間の並列
+%% リンク集合 $L_n$、各ノードペアの重要度 $I_n$、そして総測定予算 $C$ が
+%% 与えられる。ただし、各リンク $l_{nj}$ の真の忠実度 $f_{nj}$ は未知であ
+%% る。
+
+%% 問題の出力は測定予算内で選択された価値ある通信経路の集合である。アルゴ
+%% リズムは価値が高いと判断した $K$ 個のノードペア集合 $S_{sel}$ を決定す
+%% る。そして選択された各ノードペア $n_k$ において最も忠実度が高いと特定
+%% されたリンク $l_{nk}^*$ とその推定忠実度 $\hat{F}^*_{nk}$ を出力する。
+
+%% 本問題の目的は目的関数 ($\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}$)
+%% で定義されるネットワーク全体の総価値を最大化することである。これは選択
+%% された全経路の価値すなわち重要度と忠実度の積の総和を示す。
+
+%% \radd{このとき、制約条件は、全リンクにおける総測定コストが総測定予算
+%%   $C$ を超えないこと、すなわち 
+%%   $\sum^N_{n=1} \sum_{l \in L_n}  Cost(l) \leq C$
+%%   で与えられる。
+%% }
+
+本問題は、通信需要 (重要度 $I_n$) が異なる $N$ 個のノードペア$(S,
+D_n)$に対し、総測定予算 $C$ の制約下で、ネットワーク全体の総価値を最大
+化する測定資源配分を決定する問題である。各ノードペアは並列リン
+ク集合 $L_n$ を持ち、各リンク $l_{nj}$ の真の忠実度$f_{nj}$ は未知とす
+る。
+
+本問題は、価値が高いと判断したノードペア集合 $S_{sel}$ 選択し、
+各ペア $n_k \in S_{sel}$ で最高と推定されたリンク忠実度$F^*_{nk}$ を用
+いて、以下の目的関数で定義される総価値を最大化することである。
+{\footnotesize
+  \begin{align}
+    \text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}
+  \end{align}
+}
+
+このとき、制約条件は、全リンクにおける総測定コストが総測定予算$C$ を超
+えないこと、すなわち $\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C$で
+与えられる。
+
+
+\section{提案手法 : 二段階貪欲法(Two-Phase Greedy)による資源配分}
+
+%% 本稿では上記の問題を解くためにTwo-Phase Greedy手法を提案する。本手法は
+%% 広域的な探索と集中的な活用の二段階処理により限られた測定資源を効率的に
+%% 配分する。第一段階では全リンクに対して少量の測定を行い忠実度の初期推定
+%% 値を低コストで得る。これによりネットワーク全体の品質分布を大局的に把握
+%% する。
+
+%% 第二段階では第一段階の結果を基に残りの測定資源を価値が高いと見込まれる
+%% 有望なリンクへ集中的に投下する。具体的には各ノードペアの重要度 $I_n$
+%% と初期推定忠実度 $\hat{f}_n$ の積から価値スコアを計算する。そして価値
+%% の高いノードペア内のリンク群にのみLinkSelFiEを適用し詳細な測定を行う。
+%% この貪欲戦略により測定資源は価値創出の期待値が高い経路の特定へ自動的に
+%% 集中し総価値の効率的な最大化が期待できる。
+
+本稿では、上記の問題を解くための効率的な近似解法として、広域的な探索と
+集中的な活用を組み合わせた二段階貪欲法を提案する。この手法は、
+組合せ最適化問題に対する現実的なアプローチとして、限られた測定資源を準
+最適に配分し、計算コストを抑えつつ高い性能を実現することを目的とする。
+
+二段階貪欲法の第一段階は、広域探索フェーズである。ここでは、限ら
+れた測定予算の一部を、対象となる全てのリンクに少量ずつ均等に配分するこ
+とで、各リンクの忠実度の初期推定値を低コストで得る。
+
+本手法の第二段階は、活用フェーズである。ここでは、広域探索フェーズで得
+られた初期推定忠実度と各ノードペアの重要度の積から価値スコアを算出し、
+このスコアが高い有望なノードペア内のリンク群に残りの測定資源を集中的に
+投下する。具体的には、各ノードペア $n$ に対して価値スコア
+$I_n\hat{f}_n$を計算し、スコアの高い順にノードペアを選択する。
+
+%% そして、選
+%% 択されたノードペア内のリンク群に対してのみ、先行研究である LinkSelFiE
+%% を適用し、最も忠実度の高いリンクを高い精度で特定する。
+%% この貪欲戦略により、測定資源は価値創出の期待値が高い経路の特
+%% 定へと自動的に割り当てられ、ネットワーク全体の総価値が効率的に最大化さ
+%% れることが期待できる。
+
+
+\section{実験}
+\begin{figure}[t]
+  \centering
+  \begin{minipage}[b]{0.235\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{graphA.eps}
+    \vspace{0.5em}
+    
+    {\scriptsize 図1: 隣接ノード数3における\\測定予算と総価値スコアの関係}
+    \label{fig:r3}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[b]{0.235\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{graphC.eps}
+    \vspace{0.5em}
+    
+    {\scriptsize 図2: 隣接ノード数5における\\測定予算と総価値スコアの関係}
+    \label{fig:r5}
+  \end{minipage}
+\end{figure}
+
+本章では、提案手法がネットワーク全体の総価値を効率的に最大化できること
+を示すため、量子ネットワークシミュレータ NetSquid を用いた評価実験を行っ
+た。
+
+
+本実験では、1つの対象ノードに接続する隣接ノード数が $N=3$ および $N=5$ の2種類のスター型トポロジを用いた。各ノードペア間には5本のリンクが存在し、そのうち1本の平均忠実度を $0.95$、残りの4本を $0.85$ とする正規分布に従って忠実度を設定した。各ノードペアの重要度 $I_n$ は、区間 $[0, 1]$ の一様乱数により決定した。
+
+
+二段階貪欲法の設定として、広域探索フェーズでは、各リンクに対して
+初期予算($t_0=40$)を割り当て、全リンクを均等に測定し初期推定値を得る。
+活用フェーズでは、価値スコアによって選択されたノードペア内のリンク
+群に対して、LinkSelFiEを適用することで、最も忠実度の高いリンクを特定
+する。
+
+比較手法として、Uniform-LinkSelFiEおよびUniform-Naiveを用いた。前者は、
+LinkSelFiEの枠組みで測定予算を全ペアに均等配分し、リンクが一意に定まれ
+ばそのリンクを、そうでなければ推定忠実度が最大のリンクを選出する手法で
+ある。後者は、予算を全ペア・全リンクに均等配分する手法である。
+
+
+評価指標には、測定予算を変化させた際のネットワーク総価値スコアを用い、
+各測定予算の値について、独立なシュミレーションを 20 回実施し、その平均
+値と 95 \% 信頼区間を算出した。
+
+図1および図2の結果から、提案手法は比較手法よりも高い総価値スコアを達成し、価値の高いリンクへ優先的に資源を配分することが示された。ただし、実験で検証した範囲を超えて予算をさらに増加させた場合には、価値の低いリンクにもコストをかけてしまうため、スコアの上昇率は鈍化し、追加投資による価値の向上は限定的になると考えられる。
+
+
+%% 隣接ノードが 3 つの条件での結果 (図 1) では、
+
+%% 測定予算が少ない初期段階でスコアは急激に上昇し、その後、上昇率は緩やか
+%% になる傾向が見られた。これは、提案手法が価値の高いリンクへ優先的に資源
+%% を配分するため、初期の投資で大きな効果が得られる一方、有望なリンクの特
+%% 定が進むにつれて追加投資による価値の向上が限定的になることを示唆してい
+%% る。この結果は、特に資源制約が厳しい状況において提案手法が有効であるこ
+%% とを示している。
+
+%% また、隣接ノードが 5 つの条件での結果 (図 2) では、利用可能な予算が増
+%% えるにつれ、提案手法と比較手法との性能差がより拡大する結果が得られた。
+
+%% 探索対象となるリンクの総数が増加すると、各リンクに割り当て可能な平均測
+%% 定資源は相対的に減少し、資源配分の効率性がより重要となる。このような厳
+%% しい資源制約下において、通信需要と品質に基づいて資源を的確に配分する提
+%% 案手法の優位性がより際立つためであると考えられる。以上の結果から、提案
+%% 手法は、特に大規模で資源制約の厳しい量子ネットワークにおいて、全体の価
+%% 値を最大化する上で高い有効性を持つことが示された。
+
+
+%% 本章では、通信需要（重要度）と忠実度の両方を考慮した資源配分手法の有効
+%% 性を、シミュレーションによって定量的に評価する。具体的には、限られた測
+%% 定予算のもとで、提案手法がネットワーク全体の総価値スコア（$\sum I_n
+%%   \cdot \hat{f}_n^*$）をどれだけ効率的に最大化できるかを検証する。
+
+%% シミュレーションには、量子ネットワークシミュレータである NetSquid を用
+%% いた。評価対象とするネットワークトポロジは、1つの対象ノードと、それに
+%% 接続する隣接ノードの数が3つ（$N=3$）または5つ（$N=5$）の2種類である。
+%% 各ノードペア $(S, D_n)$ の間には、それぞれ5本の独立な量子リンクが存在
+%% すると仮定する。リンクのノイズモデルにはデポラライジングチャネルを適用
+%% し、リンク忠実度は、平均0.95のリンク1本と平均0.85のリンク4本からなる正
+%% 規分布に従って生成された。
+
+%% また、各ノードペアに割り当てられる重要度 $I_n$ は、通信タスクの優先度
+%% を表すパラメータとして、区間 $[0, 1]$ における一様乱数により設定した。
+%% なお、各評価点について20回の独立なシミュレーション試行を行い、その結果
+%% の95\%信頼区間をグラフ中に縦線で示している。
+
+%% 実験結果より、提案手法はすべての測定予算条件において比較手法よりも高い
+%% 総価値スコアを達成しており、その有効性が確認された。一方で、測定予算の
+%% 増加に伴ってスコアの上昇率は徐々に低下する傾向が見られた。これは、提案
+%% 手法が価値の高いリンクに優先的に測定資源を集中させる戦略を取るため、初
+%% 期段階において効果的な投資が行われる一方で、残されたリンク群には相対的
+%% に低い価値しか見込めないためである。この結果から、提案手法は特にリソー
+%% ス制約が厳しい状況において有効であることが示唆される。
+
+%% 図\ref{fig:r3}および図\ref{fig:r5}は、それぞれ隣接ノードが3つ（$N=3$）
+%% および5つ（$N=5$）の場合における、総価値スコアと測定予算の関係を示して
+%% いる。隣接ノード数を3から5へ増加させた場合の評価では、提案手法と比較手
+%% 法との性能差がより顕著に拡大した。隣接ノード数が増加すると、各ノードペ
+%% アに割り当て可能な平均測定資源は相対的に減少する。このような厳しい資源
+%% 制約下において、需要と品質に基づいて資源を的確に配分する提案手法の優位
+%% 性がより際立ったものと考えられる。以上の実験結果から、提案手法は通信需
+%% 要とリンク品質に基づいて測定資源を効率的に配分することにより、特に資源
+%% 制約が厳しい、あるいはネットワーク規模が大きい状況において、全体の価値
+%% を最大化する上で高い有効性を持つことが示された。
+\vspace{-0.4em}  % ← この行を追加（-0.8em 〜 -1.2em で調整）
+
+\section*{謝辞}
+本研究の一部は JSPS 科研費 24K02936 の助成を受けたものである。
+\vspace{-0.5em} % ← この行を追加
+\renewcommand{\em}{\it} \bibliographystyle{ieeetr}
+\bibliography{bib/quantum}
+\end{document}

psfix-gnuplot

@@ -0,0 +1,837 @@
+#!/usr/bin/env perl
+#
+# Fix line type and color of gnuplot-generated PostScript files.
+# Copyright (c) 2006-2015, Hiroyuki Ohsaki.
+# All rights reserved.
+#
+# $Id: psfix-gnuplot,v 1.15 2023/03/30 08:33:22 ohsaki Exp $
+#
+
+use File::Basename;
+use Getopt::Std;
+use strict;
+
+my $COLOR_FACTOR = 1.00;
+
+my %COLOR_MAP = (
+    0 => [qw(0.9 0 0)],        # red
+    1 => [qw(0.2 0.7 0)],      # green
+    2 => [qw(0 0.1 0.9)],      # blue
+    3 => [qw(0 0.8 0.8)],      # cyan
+    4 => [qw(0.6 0 0.9)],      # purple
+    5 => [qw(1 0.7 0)],        # orange
+    6 => [qw(0.5 0.5 0.5)],    # gray
+);
+
+my %POINT_MAP = (
+    'Pnt'     => 'Pnt',
+    'Pls'     => 'CircleF',
+    'Crs'     => 'BoxF',
+    'Star'    => 'DiaF',
+    'Box'     => 'TriUF',
+    'BoxF'    => 'TriDF',
+    'Circle'  => 'Circle',
+    'CircleF' => 'Box',
+    'TriU'    => 'Dia',
+    'TriUF'   => 'TriU',
+    'TriD'    => 'TriD'
+);
+
+sub usage {
+    my $prog = basename($0);
+    die <<EOF;
+usage: $prog [-e] [file...]
+  -e       change line type/color of errorbars
+EOF
+}
+
+our $opt_e;
+getopts('e') or usage();
+my $force_errorbar = $opt_e;
+
+my @buf;
+my $with_errorbar = 0;
+while (<>) {
+    chomp;
+    push @buf, $_;
+    # detect if the plot has errorbars; if the second line has a
+    # legend, it implies that the plot does not have errorbars
+    if ( /^% Begin plot #2/ .. /^% End plot #2/ ) {
+        $with_errorbar = 0 if /MRshow/;
+    }
+}
+$with_errorbar = 1 if $force_errorbar;
+
+if ($with_errorbar) {
+    # FIXME: with errorbars, only 9 lines are supported
+    %POINT_MAP = (
+        'Pnt'     => 'Pnt',
+        'Pls'     => 'CircleF',
+        'Crs'     => 'CircleF',
+        'Star'    => 'BoxF',
+        'Box'     => 'BoxF',
+        'BoxF'    => 'DiaF',
+        'Circle'  => 'DiaF',
+        'CircleF' => 'TriUF',
+        'TriU'    => 'TriUF',
+        'TriUF'   => 'TriDF',
+        'TriD'    => 'TriDF',
+        'TriDF'   => 'Circle',
+        'Dia'     => 'Circle',
+        'DiaF'    => 'Box',
+        'Pent'    => 'Box',
+        'PentF'   => 'Dia',
+        'C0'      => 'Dia'
+    );
+}
+
+for (@buf) {
+    # line color
+    if (m:^/LC(\w+) \{([\d.]+) ([\d.]+) ([\d.]+)\} def$:) {
+        my ( $color_number, $r, $g, $b ) = ( $1, $2, $3, $4 );
+        my $n = $color_number;
+        if ( $with_errorbar and $n > 0 ) {
+            $n = int( $color_number / 2 );
+        }
+        if ( exists $COLOR_MAP{$n} ) {
+            ( $r, $g, $b ) = map { $_ * $COLOR_FACTOR } @{ $COLOR_MAP{$n} };
+        }
+        $_ = "/LC$color_number {$r $g $b} def";
+    }
+
+    # point data
+    if (/^([\d.]+) ([\d.]+) (\w+)$/) {
+        my ( $x, $y, $pnt ) = ( $1, $2, $3 );
+        if ( exists $POINT_MAP{$pnt} ) {
+            $_ = "$x $y $POINT_MAP{$pnt}";
+        }
+    }
+
+    print "$_\n";
+}
+
+__END__
+
+gnuplot-4.0.0/term/post.trm:
+
+"/LT0 { PL [] 1 0 0 DL } def\n",
+"/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def\n",
+"/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def\n",
+"/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def\n",
+"/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def\n",
+"/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def\n",
+"/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def\n",
+"/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def\n",
+"/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def\n",
+
+/* postscript point routines */
+
+TERM_PUBLIC void
+PS_point(x,y,number)
+unsigned int x,y;
+int number;
+{
+    static const char GPFAR * GPFAR pointFNS[] = {
+	"Pnt",  "Pls",   "Crs",    "Star",
+	"Box",  "BoxF",  "Circle", "CircleF",
+	"TriU", "TriUF", "TriD",   "TriDF",
+	"Dia",  "DiaF",  "Pent",   "PentF",
+	"C0",   "C1",    "C2",     "C3",
+	"C4",   "C5",    "C6",     "C7",
+	"C8",   "C9",    "C10",    "C11",
+	"C12",  "C13",   "C14",    "C15",
+	"S0",   "S1",    "S2",     "S3",
+	"S4",   "S5",    "S6",     "S7",
+	"S8",   "S9",    "S10",    "S11",
+	"S12",  "S13",   "S14",    "S15",
+	"D0",   "D1",    "D2",     "D3",
+	"D4",   "D5",    "D6",     "D7",
+	"D8",   "D9",    "D10",    "D11",
+	"D12",  "D13",   "D14",    "D15",
+	"BoxE", "CircE", "TriUE",  "TriDE",
+	"DiaE", "PentE", "BoxW",   "CircW",
+	"TriUW", "TriDW", "DiaW",  "PentW"
+};
+
+gnuplot-4.2.2/term/post.trm:
+
+% Default Line colors
+/LCw {1 1 1} def
+/LCb {0 0 0} def
+/LCa {0 0 0} def
+/LC0 {1 0 0} def
+/LC1 {0 1 0} def
+/LC2 {0 0 1} def
+/LC3 {1 0 1} def
+/LC4 {0 1 1} def
+/LC5 {1 1 0} def
+/LC6 {0 0 0} def
+/LC7 {1 0.3 0} def
+/LC8 {0.5 0.5 0.5} def
+% Default Line Types
+/LTw {PL [] 1 setgray} def
+/LTb {BL [] LCb DL} def
+/LTa {AL [1 udl mul 2 udl mul] 0 setdash LCa setrgbcolor} def
+/LT0 {PL [] LC0 DL} def
+/LT1 {PL [4 dl1 2 dl2] LC1 DL} def
+/LT2 {PL [2 dl1 3 dl2] LC2 DL} def
+/LT3 {PL [1 dl1 1.5 dl2] LC3 DL} def
+/LT4 {PL [6 dl1 2 dl2 1 dl1 2 dl2] LC4 DL} def
+/LT5 {PL [3 dl1 3 dl2 1 dl1 3 dl2] LC5 DL} def
+/LT6 {PL [2 dl1 2 dl2 2 dl1 6 dl2] LC6 DL} def
+/LT7 {PL [1 dl1 2 dl2 6 dl1 2 dl2 1 dl1 2 dl2] LC7 DL} def
+/LT8 {PL [2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def
+/Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def
+/Dia {stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  Pnt} def
+/Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+ } def
+/Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  Pnt} def
+/Crs {stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke} def
+/TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  Pnt} def
+/Star {2 copy Pls Crs} def
+/BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath fill} def
+/TriUF {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath fill} def
+/TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath stroke
+  Pnt} def
+/TriDF {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath fill} def
+/DiaF {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath fill} def
+/Pent {stroke [] 0 setdash 2 copy gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath stroke grestore Pnt} def
+/PentF {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath fill grestore} def
+/Circle {stroke [] 0 setdash 2 copy
+  hpt 0 360 arc stroke Pnt} def
+/CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def
+/C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def
+/C1 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C2 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C3 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C4 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 180 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C5 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc
+	2 copy moveto
+	2 copy vpt 180 270 arc closepath fill
+	vpt 0 360 arc} bind def
+/C6 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C7 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C8 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 270 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C9 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 270 450 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
+	2 copy moveto
+	2 copy vpt 90 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C11 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 180 arc closepath fill
+	2 copy moveto
+	2 copy vpt 270 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C12 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 180 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C13 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc closepath fill
+	2 copy moveto
+	2 copy vpt 180 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C14 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 360 arc closepath fill
+	vpt 0 360 arc} bind def
+/C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
+	neg 0 rlineto closepath} bind def
+/Square {dup Rec} bind def
+/Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def
+/S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def
+/S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def
+/S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
+/S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def
+/S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
+/S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill
+	exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
+/S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def
+/S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
+	2 copy vpt Square fill Bsquare} bind def
+/S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def
+/S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def
+/S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
+	Bsquare} bind def
+/S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
+	Bsquare} bind def
+/S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def
+/S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
+	2 copy vpt Square fill Bsquare} bind def
+/S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
+	2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
+/S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def
+/D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def
+/D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def
+/D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def
+/D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def
+/D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def
+/D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def
+/D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def
+/D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def
+/D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def
+/D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def
+/D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def
+/D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def
+/D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def
+/D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def
+/D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def
+/D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def
+/DiaE {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke} def
+/BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke} def
+/TriUE {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke} def
+/TriDE {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath stroke} def
+/PentE {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath stroke grestore} def
+/CircE {stroke [] 0 setdash 
+  hpt 0 360 arc stroke} def
+/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def
+/DiaW {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V Opaque stroke} def
+/BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V Opaque stroke} def
+/TriUW {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V Opaque stroke} def
+/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V Opaque stroke} def
+/PentW {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  Opaque stroke grestore} def
+/CircW {stroke [] 0 setdash 
+  hpt 0 360 arc Opaque stroke} def
+/BoxFill {gsave Rec 1 setgray fill grestore} def
+/Density {
+  /Fillden exch def
+  currentrgbcolor
+  /ColB exch def /ColG exch def /ColR exch def
+  /ColR ColR Fillden mul Fillden sub 1 add def
+  /ColG ColG Fillden mul Fillden sub 1 add def
+  /ColB ColB Fillden mul Fillden sub 1 add def
+  ColR ColG ColB setrgbcolor} def
+/BoxColFill {gsave Rec PolyFill} def
+/PolyFill {gsave Density fill grestore grestore} def
+/h {rlineto rlineto rlineto gsave fill grestore} bind def
+
+gnuplot-5.0.5+dfsg1/term/post.trm:
+
+%
+% Gnuplot Prolog Version 5.1 (Oct 2015)
+%
+%/SuppressPDFMark true def
+%
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/N {newpath moveto} bind def
+/Z {closepath} bind def
+/C {setrgbcolor} bind def
+/f {rlineto fill} bind def
+/g {setgray} bind def
+/Gshow {show} def   % May be redefined later in the file to support UTF-8
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow {currentpoint stroke M 0 vshift R 
+	Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def
+/Rshow {currentpoint stroke M dup stringwidth pop neg vshift R
+	Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def
+/Cshow {currentpoint stroke M dup stringwidth pop -2 div vshift R 
+	Blacktext {gsave 0 setgray textshow grestore} {textshow} ifelse} def
+/UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
+  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def
+/DL {Color {setrgbcolor Solid {pop []} if 0 setdash}
+ {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse} def
+/BL {stroke userlinewidth 2 mul setlinewidth
+	Rounded {1 setlinejoin 1 setlinecap} if} def
+/AL {stroke userlinewidth 2 div setlinewidth
+	Rounded {1 setlinejoin 1 setlinecap} if} def
+/UL {dup gnulinewidth mul /userlinewidth exch def
+	dup 1 lt {pop 1} if 10 mul /udl exch def} def
+/PL {stroke userlinewidth setlinewidth
+	Rounded {1 setlinejoin 1 setlinecap} if} def
+3.8 setmiterlimit
+% Classic Line colors (version 5.0)
+/LCw {1 1 1} def
+/LCb {0 0 0} def
+/LCa {0 0 0} def
+/LC0 {0.9 0 0} def
+/LC1 {0.2 0.7 0} def
+/LC2 {0 0.1 0.9} def
+/LC3 {0 0.8 0.8} def
+/LC4 {0.6 0 0.9} def
+/LC5 {1 0.7 0} def
+/LC6 {0.5 0.5 0.5} def
+/LC7 {1 0.3 0} def
+/LC8 {0.5 0.5 0.5} def
+% Default dash patterns (version 5.0)
+/LTB {BL [] LCb DL} def
+/LTw {PL [] 1 setgray} def
+/LTb {PL [] LCb DL} def
+/LTa {AL [1 udl mul 2 udl mul] 0 setdash LCa setrgbcolor} def
+/LT0 {PL [] LC0 DL} def
+/LT1 {PL [2 dl1 3 dl2] LC1 DL} def
+/LT2 {PL [1 dl1 1.5 dl2] LC2 DL} def
+/LT3 {PL [6 dl1 2 dl2 1 dl1 2 dl2] LC3 DL} def
+/LT4 {PL [1 dl1 2 dl2 6 dl1 2 dl2 1 dl1 2 dl2] LC4 DL} def
+/LT5 {PL [4 dl1 2 dl2] LC5 DL} def
+/LT6 {PL [1.5 dl1 1.5 dl2 1.5 dl1 1.5 dl2 1.5 dl1 6 dl2] LC6 DL} def
+/LT7 {PL [3 dl1 3 dl2 1 dl1 3 dl2] LC7 DL} def
+/LT8 {PL [2 dl1 2 dl2 2 dl1 6 dl2] LC8 DL} def
+/SL {[] 0 setdash} def
+/Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def
+/Dia {stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  Pnt} def
+/Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+ } def
+/Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  Pnt} def
+/Crs {stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke} def
+/TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  Pnt} def
+/Star {2 copy Pls Crs} def
+/BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath fill} def
+/TriUF {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath fill} def
+/TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath stroke
+  Pnt} def
+/TriDF {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath fill} def
+/DiaF {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath fill} def
+/Pent {stroke [] 0 setdash 2 copy gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath stroke grestore Pnt} def
+/PentF {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath fill grestore} def
+/Circle {stroke [] 0 setdash 2 copy
+  hpt 0 360 arc stroke Pnt} def
+/CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def
+/C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def
+/C1 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C2 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C3 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C4 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 180 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C5 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc
+	2 copy moveto
+	2 copy vpt 180 270 arc closepath fill
+	vpt 0 360 arc} bind def
+/C6 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C7 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 270 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C8 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 270 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C9 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 270 450 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
+	2 copy moveto
+	2 copy vpt 90 180 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C11 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 180 arc closepath fill
+	2 copy moveto
+	2 copy vpt 270 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C12 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 180 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C13 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 0 90 arc closepath fill
+	2 copy moveto
+	2 copy vpt 180 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/C14 {BL [] 0 setdash 2 copy moveto
+	2 copy vpt 90 360 arc closepath fill
+	vpt 0 360 arc} bind def
+/C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
+	vpt 0 360 arc closepath} bind def
+/Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
+	neg 0 rlineto closepath} bind def
+/Square {dup Rec} bind def
+/Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def
+/S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def
+/S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def
+/S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
+/S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def
+/S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
+/S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill
+	exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
+/S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def
+/S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
+	2 copy vpt Square fill Bsquare} bind def
+/S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def
+/S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def
+/S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
+	Bsquare} bind def
+/S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
+	Bsquare} bind def
+/S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def
+/S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
+	2 copy vpt Square fill Bsquare} bind def
+/S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
+	2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
+/S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def
+/D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def
+/D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def
+/D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def
+/D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def
+/D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def
+/D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def
+/D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def
+/D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def
+/D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def
+/D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def
+/D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def
+/D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def
+/D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def
+/D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def
+/D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def
+/D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def
+/DiaE {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke} def
+/BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke} def
+/TriUE {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke} def
+/TriDE {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V closepath stroke} def
+/PentE {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  closepath stroke grestore} def
+/CircE {stroke [] 0 setdash 
+  hpt 0 360 arc stroke} def
+/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def
+/DiaW {stroke [] 0 setdash vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V Opaque stroke} def
+/BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V Opaque stroke} def
+/TriUW {stroke [] 0 setdash vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V Opaque stroke} def
+/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M
+  hpt neg vpt 1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt -1.62 mul V Opaque stroke} def
+/PentW {stroke [] 0 setdash gsave
+  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+  Opaque stroke grestore} def
+/CircW {stroke [] 0 setdash 
+  hpt 0 360 arc Opaque stroke} def
+/BoxFill {gsave Rec 1 setgray fill grestore} def
+/Density {
+  /Fillden exch def
+  currentrgbcolor
+  /ColB exch def /ColG exch def /ColR exch def
+  /ColR ColR Fillden mul Fillden sub 1 add def
+  /ColG ColG Fillden mul Fillden sub 1 add def
+  /ColB ColB Fillden mul Fillden sub 1 add def
+  ColR ColG ColB setrgbcolor} def
+/BoxColFill {gsave Rec PolyFill} def
+/PolyFill {gsave Density fill grestore grestore} def
+/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def
+%
+% PostScript Level 1 Pattern Fill routine for rectangles
+% Usage: x y w h s a XX PatternFill
+%	x,y = lower left corner of box to be filled
+%	w,h = width and height of box
+%	  a = angle in degrees between lines and x-axis
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qnet.org

@@ -0,0 +1,1788 @@
+** Q. 以下の論文が解いている問題の入力、出力、制約条件、目的関数を説明して
+
+IEEE INFOCOM 2024 - IEEE Conference on Computer Communications | 979-8-3503-8350-8/24/$31.00 ©2024 IEEE | DOI: 10.1109/INFOCOM52122.2024.10621263
+
+L INK S EL F I E: Link Selection and Fidelity
+Estimation in Quantum Networks
+Maoli Liu, Zhuohua Li⇤ , Xuchuang Wang, John C.S. Lui
+The Chinese University of Hong Kong
+{mlliu, zhli, xcwang, cslui}@cse.cuhk.edu.hk
+
+Abstract—Reliable transmission of fragile quantum information
+requires one to efficiently select and utilize high-fidelity links
+among multiple noisy quantum links. However, the fidelity, a
+quality metric of quantum links, is unknown a priori. Uniformly
+estimating the fidelity of all links can be expensive, especially
+in networks with numerous links. To address this challenge, we
+formulate the link selection and fidelity estimation problem as
+a best arm identification problem and propose an algorithm
+named L INK S EL F I E. The algorithm efficiently identifies the
+optimal link from a set of quantum links and provides an
+accurate fidelity estimate of that link with low quantum resource
+consumption. L INK S EL F I E estimates link fidelity based on
+the feedback of a vanilla network benchmarking subroutine,
+and adaptively eliminates inferior links throughout the whole
+fidelity estimation process. This elimination leverages a novel
+confidence interval derived in this paper for the estimates from
+the subroutine, which theoretically guarantees that L INK S EL F I E
+outputs the optimal link correctly with high confidence. We
+also establish a provable upper bound of cost complexity for
+L INK S EL F I E. Moreover, we perform extensive simulations under
+various scenarios to corroborate that L INK S EL F I E outperforms
+other existing methods in terms of both identifying the optimal
+link and reducing quantum resource consumption.
+Index Terms—Quantum Networks, Link Selection, Fidelity
+Estimation
+
+I. I NTRODUCTION
+Quantum networks are capable of transmitting quantum information, represented by quantum bits or qubits, between multiple
+quantum systems, facilitating groundbreaking applications
+such as quantum cryptography [1], quantum key distribution
+(QKD) [2], clock synchronisation [3], and quantum internetof-things (QIoT) [4]. The principles of quantum mechanics [5]
+enable quantum networks to achieve functionalities that remain
+unattainable with classical networks. However, harnessing the
+potential of quantum networks also introduces new challenges
+in network design and benchmarking. For instance, direct
+transmission of qubits via physical quantum links, such as
+optical fibers, in a large-scale quantum network is not feasible, as the probability of successful transmission diminishes
+exponentially with the length of quantum links due to quantum
+decoherence. Additionally, the no-cloning theorem [6] prevents
+the replication of an arbitrary qubit for re-transmission or
+amplification, adding further complexity to quantum network
+design. Besides, quantum information is inherently fragile and
+easily corrupted by noise, necessitating the benchmarking of
+quantum networks to ensure their reliability and performance.
+⇤ Zhuohua Li is the corresponding author. The work of John C.S. Lui was
+supported in part by the RGC GRF 14207721.
+
+A quantum network usually consists of quantum nodes
+connected via quantum links [7]. Each quantum node can
+function as a source, a destination, or a repeater, with the
+ability to perform quantum operations and store qubits in its
+quantum memory. Quantum links, often formed by optical fibers
+or free-space optical links, can deliver qubits from one end to
+the other. To realize long-distance qubit transmission, people
+rely on quantum entanglement, a phenomenon where multiple
+qubits are correlated and the state of individual qubits cannot be
+described independently of the others. Quantum entanglement
+is regarded as an important resource for transmitting quantum
+information. Various experiments [8]–[10] have successfully
+demonstrated the distribution of quantum entanglement. Once
+two quantum nodes share entangled pairs, they can transmit
+quantum information to each other by a process known as
+quantum teleportation [11], regardless of their distance.
+Reliable long-distance quantum information transmission
+is a fundamental requirement for many quantum applications.
+Many existing works [12]–[15] focus on long-distance quantum entanglement routing protocols. These protocols aim to
+establish end-to-end entanglement through quantum repeaters
+via an operation called entanglement swapping [11], [16] in a
+quantum network, with the goal of improving the network
+throughput, enhancing robustness and serving more users.
+However, due to the fragile nature of quantum information,
+qubits are susceptible to decoherence via interactions with the
+environment. For example, the generated entangled pairs may
+not be perfectly entangled, and attenuation in physical links
+and imperfect swapping operations may lead to corruption
+during the establishment of long-distance entanglement. As
+a result, the established end-to-end entanglement may not be
+at the desired states and cannot be used for reliable quantum
+information transmission. Usually, people use fidelity [5] to
+quantify the quality of an entanglement link. The value of
+fidelity is from 0 to 1, and it measures how well a quantum
+channel preserves quantum information. Despite some recent
+works [17]–[19] that take fidelity guarantee into consideration
+when designing entanglement routing protocols, it remains
+essential to explicitly verify the quality of entanglement links
+before transmitting important quantum information.
+The main objective of this work is to efficiently estimate the
+fidelity of established entangled links. Our approach is based on
+a method called network benchmarking [20], which measures
+the average fidelity of quantum entanglement links. However,
+network benchmarking is designed to measure a single quantum
+
+Authorized licensed use limited to:©2024
+Chinese University
+of Hong Kong. Downloaded
+979-8-3503-8350-8/24/$31.00
+IEEE
+1421on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+link. In cases where there are multiple links with unknown
+fidelities—a common scenario in quantum communications, one
+needs to apply network benchmarking to each link individually,
+S
+S
+S
+D
+D
+D
+leading to a rather high cost. In practice, one only needs to
+(b) Entanglement Swapping
+(c) End-to-End Entanglement
+(a) Entanglement Generation
+select a few high-fidelity quantum links to transmit quantum
+information. Precise fidelity estimation of links with low fidelity
+Repeater
+Entanglement
+Physical Link
+Qubit
+Swapping
+is unnecessary where the corresponding benchmarking cost
+Fig. 1. End-to-end entanglement establishment.
+is actually a waste and can be partially saved. Therefore, we
+consider identifying and eliminating low-fidelity links early on
+from a set of unknown links, so that we can efficiently obtain
+efficient decision-making with limited quantum resources.
+accurate fidelity estimates for the desired high-quality links
+• We propose a new algorithm named L INK S EL F I E, which
+and save quantum resources.
+utilizes the novel confidence interval for the network
+To tackle the challenging problem of link selection and
+benchmarking subroutine. We prove that our algorithm can
+fidelity estimation, we formulate it as a best arm identification
+correctly output the optimal link and its accurate fidelity
+problem, a classical sequential decision-making task in multiestimate with high probability. Additionally, we provide a
+armed bandits [21]. Specifically, each arm corresponds to an
+provable cost complexity upper bound for the algorithm.
+entangled link in a link set, and each arm is associated with an
+• We conduct extensive simulations, and the results show
+unknown stochastic reward representing the link fidelity. The
+that L INK S EL F I E can identify optimal links with signetwork benchmarking method requires transmitting qubits
+nificantly fewer quantum resources compared to other
+through a link multiple times to obtain a fidelity estimate,
+methods while providing comparable fidelity estimation
+which implies that one can only receive a reward or feedback
+accuracy.
+after pulling an arm multiple times. This poses a significant
+The rest of the paper is organized as follows. We first present
+challenge compared to the classical setting, where a single pull
+of an arm yields an immediate reward sample. Our objective some background information on quantum networks and the
+is to identify the link with the highest fidelity from a link set network benchmarking method in Section II. In Section III,
+and get its fidelity estimate while consuming as few quantum We formulate the link selection and fidelity estimation problem
+resources as possible. To achieve this, we design a phase-based as a best arm identification problem. The detailed algorithm
+elimination algorithm named L INK S EL F I E (Link Selection and design and its theoretical analysis are presented in Section IV.
+Fidelity Estimation). The elimination utilizes a novel confidence Performance evaluations of our algorithm are conducted in
+interval derived in this paper for the results of the vanilla Section V, and related work is discussed in Section VI. Finally,
+network benchmarking subroutine. Based on the confidence Section VII concludes the paper.
+interval, we prove that our algorithm identifies the optimal link
+II. BACKGROUND
+with high confidence. We also introduce the notion of cost
+In this section, we review some prerequisites about quantum
+complexity, which corresponds to quantum resources used by
+the algorithm and provide a cost complexity upper bound of networks and the network benchmarking method [20].
+our algorithm, which theoretically shows that our algorithm
+is more efficient than the vanilla network benchmarking [20]. A. Quantum Networks
+A quantum network is composed of quantum nodes interconTo evaluate our algorithm, we simulate a quantum network
+where a pair of quantum nodes are connected via multiple nected via quantum links. Each quantum node typically contains
+entanglement links associated with different levels of noise. a quantum processor for performing quantum operations and
+Our goal is to determine the link with the highest fidelity. measurements and has the ability to generate and store quantum
+We conduct simulations with different noise models and link states in its limited quantum memory. Quantum links, which
+fidelity distributions. The results corroborate that our algorithm can be optical fibers or free-space optical links, facilitate the
+significantly reduces the total benchmarking cost compared physical transmission of qubits between quantum nodes, such as
+to the vanilla network benchmarking method and the naive the transmission of photons through an optical fiber. However,
+successive elimination method. Furthermore, our L INK S EL F I E since the successful transmission rate decreases exponentially
+algorithm operates without requiring any knowledge of the with the length of quantum links, people have proposed
+network topology or the entanglement generation process. entanglement-based networks and use quantum entanglement
+Therefore it can be easily integrated into the current multi- to enhance the transmission of quantum information.
+1) End-to-End Entanglement: Quantum entanglement arises
+layer design of the quantum network protocol stack. This
+adaptability allows it to seamlessly function with different when the shared state between multiple qubits cannot be
+lower-level protocols, such as entanglement routing or network factored into a product of its individual qubit states. A
+classical example is the maximally entangled EPR (Einsteindiagnostic protocols.
+p
+We summarize our contributions as follows.
+Podolsky-Rosen) state | ± i = |01i±|10i
+. To overcome the
+2
+• We formulate the link selection and fidelity estimation
+distance limitation of end-to-end entanglement between two
+problem as a best arm identification problem, enabling distant quantum nodes, quantum repeaters are positioned at
+BSM
+
+BSM
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1422on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+B. Network Benchmarking
+The idea behind network benchmarking is that by channel
+twirling process [22], which involves random applications of
+Clifford operations [25], one can transform arbitrary quantum
+channels into depolarizing channels with the same fidelity.
+By accessing these depolarizing channels repeatedly, one can
+estimate the average fidelity of them, which is equivalent to
+that of the original channel. The parameters used for network
+
+Link !!
+Link !"
+
+……
+
+……
+……
+
+intermediate locations within the network. Given a source
+node S and a destination node D sharing no direct physical
+links, repeaters along a path of physical links connecting S
+and D are responsible for generating entanglement (Fig. 1
+(a)) with adjacent nodes and executing entanglement swapping
+operations (Fig. 1 (b)) to establish an end-to-end entanglement
+link between S and D (Fig. 1 (c)). After the entanglement is
+successfully established, S can teleport an information qubit
+to D by consuming that entanglement.
+2) Quantum Noise and Average Fidelity: When establishing
+end-to-end entanglement in quantum networks, various sources
+of noise can potentially arise. For instance, losses in optical
+fibers, imperfect hardware, and decoherence during qubit
+storage. Such noise can lead to imperfect entanglement being
+shared between the source and destination nodes, consequently
+causing errors in quantum state transmission. Quantum noise
+is often characterized by quantum channels [5]. Examples of
+noise channels include the bit-flip channel, the depolarizing
+channel, the dephasing channel, and so on. Specifically, the
+depolarizing channel E(⇢) := p⇢ + (1 p) I2 leaves the input
+quantum state ⇢ unchanged with probability p and replaces it
+with the maximally mixed state I2 (the quantum equivalent of
+a uniformly random classical bit) otherwise. The depolarizing
+channel model is a useful tool for characterizing quantum
+gates [22], [23] and quantum networks [20].
+The average fidelity [24] of a quantum link associated
+with noise channel E is defined by F (E) :=
+R
+d Tr[E(| i h |) | i h |], where the integral is taken uniformly over all pure quantum states | i and Tr denotes the trace
+of a matrix. The average fidelity quantifies how well a quantum
+link preserves information, where a fidelity of 1 corresponds
+to a noiseless channel. For quantum links corresponding to the
+depolarizing channel with parameter p, the average fidelity is
+(1 + p)/2 [5]. For simplicity, we use the term fidelity to refer
+to the average fidelity hereinafter.
+In this work, we adopt the assumption of Markovian
+noise [20], which implies that the noise is memoryless, and
+entanglement links constructed via the same path always
+correspond to the same quantum channel, irrespective of their
+prior usage history. A pair of source and destination nodes
+may be interconnected by multiple physical paths, along which
+entanglement links can be established. Consequently, each
+entanglement link between two nodes is implicitly associated
+with a specific physical path within the network. In this paper,
+we do not consider the low-level details of path discovery or
+entanglement link generation but assume the set of distinct
+entanglement links is known.
+
+S
+
+D
+Link !#
+
+Physical Quantum Link
+
+Entanglement Link
+
+Quantum Node
+
+Fig. 2. An example of a quantum network. We abstract away the irrelevant
+network topology between S and D and only assume there are L entanglement
+links.
+
+benchmarking are M and T . M is called the bounce number
+set, which contains a series of integers, and T represents the
+repetition times for each bounce number m 2 M. A “bounce”
+refers to the process in which node S applies a random Clifford
+operation to the state and sends it to node D, which then does
+the same and returns it to S. To estimate the average fidelity
+of entanglement links between nodes S and D, the following
+procedure will be implemented repeatedly for T times for each
+m 2 M: (i) source node S generates an initial state; (ii) nodes
+S and D “bounce” the state m times; (iii) source node S
+applies a final operation and measures the state. The average
+value of the T measurement results is denoted by bm , which
+is often called the survival probability. The survival probability
+is modeled by the exponential model bm = Ap2m , where A
+is a constant accounting for quantum state preparation and
+measurement errors, and p is the depolarizing parameter of
+the twirled channel. Thus, by fitting the exponential model
+bm = Ap2m to the data {M, {bm }m2M }, one can estimate
+the parameter p̂ and deduce the average fidelity (1 + p̂)/2.
+In quantum networks, transmitting a qubit over a long
+distance is costly, and each bounce consumes two entangled
+links. Therefore, we use the number of bounces as a cost metric
+for network benchmarking. In practice, it is essential not only
+to precisely estimate the fidelity of the target links but also to
+conserve the consumption of bounces.
+III. M ODEL
+In this section, we first define the link selection and
+fidelity estimation problem in quantum networks and provide
+a motivating example. Then we formulate our problem as a
+best arm identification problem in multi-armed bandits.
+A. Problem Definition
+Fig. 2 depicts a quantum network consisting of multiple
+nodes, among which we select a source node S and a
+destination node D. There are L 2 N+ entanglement links
+between S and D, denoted by L = {l1 , . . . , lL }. Each of these
+links is established along a distinct path connecting S and D.
+Note that we do not consider the underlying network topology
+or any specific mechanism for establishing these entanglement
+links, as they are irrelevant to our purposes. Instead, we abstract
+away these details and assume the existence of a network
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1423on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+protocol capable of constructing these links. The fidelities equivalent to pulling arm i for T times. Besides, the quantum
+of entanglement links can vary due to noise. We denote the resources consumed by the subroutine increase linearly in terms
+fidelity of link li 2 L by fi . The optimal links are those with of the repetition
+times T and the summation of all bounces in
+P
+the highest fidelity, i.e., l⇤ 2 arg maxli 2L fi .
+M, i.e., m2M m.
+Our goal is to design an algorithm that correctly outputs
+To ensure high-quality quantum information transmission,
+it is essential to select entanglement links with the highest the optimal arm (link) 1 with the probability of at least 1
+(confidence parameter 2 (0, 1)) with as small costs as
+fidelity. Since the link fidelities are unknown beforehand, one
+approach is to use the network benchmarking method described possible. We denote the total cost incurred by an algorithm A
+in Section II-B to estimate the fidelity of each link respectively as cost complexity, which can be expressed as follows,
+X
+X
+to a specific accuracy " > 0, i.e., |fˆi fi | < " at a given
+Cost(A) :=
+Ni,⌧
+m,
+confidence level, and then select the high-fidelity links to
+i2L
+m2M
+transmit quantum information. However, this method means
+that the benchmarking cost grows linearly with the number of where Ni,s is the total number of pulls to link i 2 L up to
+available links L. This indicates that the benchmarking cost time s, and ⌧ is the stopping time at which the algorithm A
+identifies the optimal arm.
+becomes prohibitive when the number of links is large.
+Motivating Example. A qubit may be corrupted if transmitIV. A LGORITHMS
+ted through noisy links, causing negative impacts on quantum
+In
+this
+section,
+we
+first elaborate on the design of our link
+communications. Since links with low fidelity are unsuitable for
+transmitting quantum information, it is unnecessary to spend selection and fidelity estimation algorithm, which we refer to
+resources and time on accurately estimating these inferior as L INK S EL F I E, and present the algorithmic details. We also
+links. For instance, consider two links l1 and l2 with unknown provide a theoretical analysis of its cost complexity.
+fidelities f1 = 0.9 and f2 = 0.7, respectively. When the
+estimation accuracy reaches 0.05, with a high probability the A. Algorithm Design
+Here, we propose an online algorithm (L INK S EL F I E) based
+confidence intervals of the estimate fidelities no longer overlap,
+enabling us to identify that link l2 is inferior to link l1 . Then we on multi-armed bandits results. Unlike the classical bandit
+can discard l2 , thus saving the benchmarking cost that would setting where each arm can be flexibly pulled, links in our
+have otherwise been spent on it, and focus on estimating the problem can only be pulled in “batches” by the network
+fidelity of l1 more precisely. This motivates us to explore an benchmarking subroutine. This inflexibility requires one to
+online learning approach to solve the link selection and fidelity assign multiple pulls for each link in a batched manner.
+Therefore, we consider phase-based algorithms, where in each
+estimation problem.
+phase we assign a fixed number of pulls to each link and
+B. Bandit Formulation
+run the network benchmarking subroutines to estimate their
+We now formulate the link selection and fidelity estimation fidelities. One key challenge in the algorithm design is how
+problem as a best arm identification problem. Let us consider to appropriately allocate the number of pulls to different
+a stochastic multi-armed bandit whose arm set is denoted as phases, which shall (a) be based on the theoretical estimation
+K := {1, . . . , L}. Each arm i 2 K corresponds to a distinct performance of this subroutine (see Lemma 1), and also (b) be
+link in li 2 L. The reward of each arm i 2 K is associated with adaptive to the relative magnitudes of all links fidelities (e.g.,
+a stochastic random variable Pi , whose mean is pi , satisfying reward gaps i ), which are unknown a priori.
+To address this challenge, we propose a phase-based elimthat fi = (pi + 1)/2 and pi 2 (0, 1), i.e., there is a simple
+linear relation between the link fidelities and reward means. ination algorithm, presented in Algorithm 1. The algorithm
+Without loss of generality, we assume that reward means are runs in phases denoted as s = 0, 1, 2, . . . and proceeds with a
+sorted in descending order, i.e., p1 > p2 > · · · > pL , and arm link elimination mechanism. In the beginning, the algorithm
+1 is the unique optimal arm, since one can always relabel the initializes a candidate set S as the full link set L. In each
+link index. We denote the reward mean gaps as i := p1 pi phase, the algorithm executes the vanilla network benchmarking
+subroutines for all remaining links in the candidate set S with
+for suboptimal arm i 6= 1, and for i = 1, we set 1 = 2 .
+In the stochastic multi-armed bandit, the decision maker appropriate pull times Ts according to Lemma 1 (address (a)).
+obtains samples drawn from the reward distribution of an arm At the end of each phase, the algorithm eliminates the inferior
+by pulling that arm. The empirical reward mean can then be links identified in this phase, and, therefore, the algorithm does
+estimated by averaging multiple samples of the arm. However, not need to spend costs on these inferior links (adaptively) in
+in the fidelity estimation of quantum entanglement links, the future phases (address (b)).
+L INK S EL F I E takes three input parameters: the link set L,
+empirical reward (fidelity estimate) is computed via regression
+by the vanilla network benchmarking subroutine. This implies the pre-configured bounce length set M, and the confidence
+that in our specific scenario, arms (links) can only be pulled parameter 2 (0, 1). Ts is the cumulative number of pulls for
+in batches. For simplicity, we regard the act of applying this remaining links in S in phase s, i.e., the assigned number
+Ts 1 . We set
+vanilla network benchmarking subroutine with the bounce of pulls for one link in phase s is Ts
+number set M and the repetition times T to link li once Ts = C22s log s(s+1)|S| (Line 3), where C is a constant in
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1424on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+(s)
+
+Lemma 1. Let p̂i be the estimate fidelity of link i in phase
+(s)
+s and bi,m be the empirical survival probability of link i
+at the bounce number m after Ts trials. We integrate the
+vanilla network benchmarking illustrated in Section II-B as a
+subroutine here, i.e., Benchmarking (Line 5). The subroutine
+Fitting (Line 7) fits the model bm = Ap2m to the input
+data and returns p̂.
+Specifically, at the beginning of each phase s, L INK S EL F I E
+uniformly pulls links in the candidate set that have not been
+eliminated yet for Ts Ts 1 times (i.e., run the network
+benchmarking subroutine with the repetition times Ts Ts 1
+(s)
+(Line 5)). Following this, it calculates bi,m by weighted
+(s 1)
+averaging the newly obtained data bi,m and the data bi,m
+(s)
+from last phase (Line 6), and gets fidelity estimates p̂i of
+the remaining links (Line 7). Then it determines the maximum
+estimate value p̂max (Line 8) and discards links i satisfying the
+(s)
+condition p̂i + 2 s < p̂max 2 s (Line 9). The condition
+means that the upper confidence bound of link i is less than
+the lower confidence bound of the link with the current highest
+empirical fidelity, which implies that link i is a suboptimal
+link with high confidence and we can eliminate link i. When
+there is only one link left in the candidate set S, the algorithm
+terminates and returns corresponding information.
+Algorithm 1: LinkSelFiE: Link Selection & Fidelity Estimation
+
+Input: path set L, confidence parameter , bounce
+length set M
+Initialization: candidate set S
+L, s
+0,
+(0)
+p̂i
+0, 8i 2 L, T0 = 0,
+(0)
+bi,m = 0, 8i 2 L, m 2 M
+1 while |S| > 1 do
+2
+s
+s + 1 // s is the current phase.
+3
+Ts
+C · 22s log s(s+1)|S| // C is a
+constant.
+4
+for i 2 S do
+5
+{bi,m }m2M
+Benchmarking(i, M, Ts Ts 1 )
+6
+7
+
+(s)
+
+bi,m
+(s)
+p̂i
+
+bi,m (Ts Ts
+
+(s
+
+1)
+
+1 )+bi,m Ts 1
+,8m 2 M
+Ts
+(s)
+Fitting(M, {bi,m }m2M )
+
+(s)
+
+p̂max
+maxi2S p̂i
+(s)
+9
+S
+S \ {i 2 S : p̂i + 2 s 6 p̂max 2 s }
+Output: the remaining link in S and p̂max
+8
+
+B. Theoretical Analysis
+In this subsection, We analyze the cost complexity upper
+bound of L INK S EL F I E.
+We begin by presenting the confidence interval for the
+estimate of the vanilla network benchmarking method described
+in Section II-B. Since the link fidelity is estimated from an
+exponential regression using data points of each bounce length
+m 2 M, rather than a simple average of independent random
+samples, directly applying the conventional analysis tools used
+
+in classical bandit literature, such as Hoeffding’s inequality,
+fails to capture the correlations between data, and thus yields a
+looser confidence interval. To address this issue, we examine the
+properties of non-linear regression and derive a new confidence
+interval in Lemma 1, which exploits information from all
+data points of each bounce length, offering an advantage over
+Hoeffding’s inequality.
+Lemma 1 (Confidence Interval for Network Benchmarking).
+Given the input parameters M and T 2 N+ , for a confidence
+parameter 2 (0, 1), to benchmark a link with the true depolarizing parameter p, the depolarizing parameter p̂ estimated
+by the vanilla network benchmarking method satisfies,
+"
+#
+r
+C
+1
+Pr |b
+p p| 6
+log
+>1
+,
+T
+where C is a constant related to the bounce length set M and
+measurement noise, which is explicitly expressed in Appendix A.
+We refer interested readers to Appendix A for its detailed
+proof. Given Lemma 1, we have the following corollary.
+Corollary 1. Given the confidence radius " and the confidence
+level 1 , the required repetition times for the vanilla network
+benchmarking method should satisfy:
+✓
+◆
+C
+1
+T =O
+log
+.
+"2
+
+From Corollary 1, we know how to set the repetition
+times T to achieve certain accuracy when benchmarking one
+entanglement link, which also implies the benchmarking cost.
+Based on the above lemma, we derive a cost complexity
+upper bound for our Algorithm 1. The proof details of
+Theorem 1 is given in Appendix B.
+Theorem 1 (Cost Complexity of Algorithm 1). Given a bounce
+length set M and a confidence parameter 2 (0, 1), the cost
+complexity of Algorithm 1 is upper bounded as follows,
+✓
+◆! X
+X C
+L
+4
+Cost(AL INK S EL F I E ) 6 O
+log
+·
+m,
+2 log
+i2L
+
+i
+
+i
+
+m2M
+
+where L is the number of links and C is a universal constant.
+
+Remark 1 (Modify Algorithm 1 to find an "-optimal link). If we
+modify the algorithm proceeding condition in Line 1 to be more
+than one link remains in the candidate set and the estimation
+accuracy does not reach ", i.e., |S| > 1 and 2 s > ", then
+Algorithm 1 can output "-optimal links (whose fidelity is greater
+than the optimal one minus ", i.e., pi > p1 "). Identifying such
+"-optimal links is often practical in quantum networks [17].
+With this modification, the cost complexity is upper bounded
+as follows,
+✓
+◆! X
+X C
+L
+4
+Cost(Amod ) 6 O
+log
+log
+·
+m, (1)
+˜2
+˜i
+i2L
+
+where e i := max{
+
+i
+
+m2M
+
+i , "}.
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1425on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+Remark 2 (Compare to vanilla network benchmarking (uniform
+exploration)). If one applies the vanilla network benchmarking
+method to uniformly estimate all links’ fidelities and stops
+at the accuracy ", then the cost complexity would be upper
+bounded as follows,
+✓
+◆ X
+CL
+L
+Cost(Avanilla ) 6 O
+log
+·
+m.
+"2
+m2M
+
+The above bound is greater than (1) especially when there are
+some links with large fidelity gaps i . This corresponds to
+that when i ’s are large, Algorithm 1 can eliminate these links
+with high fidelity gaps in early phases, thereby conserving a
+large number of quantum resources.
+V. P ERFORMANCE E VALUATION
+
+In this section, we evaluate our algorithm L INK S EL F I E. We
+first elaborate on our experiment setups, including quantum
+network structure, quantum noise model, baseline algorithms,
+and the performance metrics we use. Then, we show our
+evaluation results in terms of efficiency and precision.
+A. Experiment Setup
+
+and simulate a two-node quantum network with L links,
+which have fidelities 1, 1
+, 1 2 , . . . , 1 (L 1) ,
+respectively. Then we apply each link selection algorithm
+to the network for different values of L and measure the
+quantum resource consumption when the algorithms terminate.
+Note that we use the total number of bounces as the metric
+for quantum resource consumption and average the results
+over 10 trials. Figure 3 shows the plots of quantum resource
+consumption versus the number of links under different noise
+models. Since VanillaNB spends the same amount of resources
+for each link, its resource consumption is proportional to
+the number of links in the network. This leads to excessive
+resource waste when the network has many low-quality links.
+On the other hand, both L INK S EL F I E and SuccElimNB can
+adaptively decide the resources spent by each link, and the
+cost complexity grows slowly as L increases because it mainly
+depends on the fidelity gap . However, SuccElimNB only
+relies on Hoefdding’s inequality to estimate the confidence
+interval, while L INK S EL F I E benefits from the much tighter
+confidence intervals for the non-linear regression (Lemma 1).
+Therefore, L INK S EL F I E collects sufficient information and
+eliminates the inferior arms more efficiently. The numerical
+results demonstrate that L INK S EL F I E costs significantly fewer
+resources than the other two algorithms.
+
+We evaluate our algorithm by simulating a quantum network
+with two nodes connected via several quantum entanglement
+links. We employ various common noise models and assign
+different levels of noise to the quantum links, and the objective
+is to identify the optimal link using as few quantum resources
+as possible. The entanglement links are generated by placing a
+quantum source in the middle and bidirectionally distributing
+entangled photon pairs through noisy quantum channels. We
+apply four standard and widely used noise models to simulate
+quantum noise [5]: (1) depolarizing noise model, (2) dephasing
+noise model, (3) amplitude damping noise model, and (4) bit
+flip noise model. For the sake of fair comparison among these
+(a) Depolarizing Noise
+(b) Dephasing Noise
+noise models, given a fidelity value, we convert it into the
+corresponding noise parameters used to initialize each noise
+model. All the quantum mechanisms are simulated by an offthe-shelf quantum network simulation framework called NetSquid [26]. We compare our algorithm with two baselines, (1)
+the vanilla network benchmarking algorithm (VanillaNB) and
+(2) the successive elimination algorithm [27] (SuccElimNB).
+VanillaNB uniformly benchmarks all the quantum links for
+each bounce number with a fixed number of repetitions T ,
+(c) Amplitude Damping Noise
+(d) Bit Flip Noise
+which we set to T = 200 in our experiments. SuccElimNB
+Fig. 3. Bounces v.s. the number of links L using different noise models.
+invokes the network benchmarking subroutine with repetition
+times T = 4 and treats the estimated fidelities as independent
+Next, we examine the effect of the fidelity gap on the
+random samples, then it makes optimistic decisions based on
+upper confidence bounds derived via Hoefdding’s inequality. It performance of the link selection algorithms. The fidelity gap
+iteratively eliminates identified bad links as learning proceeds reflects the hardness of the best arm identification problem.
+until there is only one link left. All the experiments were done We fix the number of links L = 4 and vary the fidelity gap
+, and we plot the quantum resource consumption versus the
+on a Linux machine (kernel 6.1.38) with a 3.70 GHz Intel
+fidelity gap under different noise models, averaged over 10
+Xeon E5-1630 v4 CPU and 16GB RAM.
+trials. As shown in Figure 4, the cost of VanillaNB is preB. Quantum Resources Consumption
+determined so it is not affected by the fidelity gap, while
+First, we evaluate the quantum resource consumption of L INK S EL F I E and SuccElimNB can adaptively adjust the cost
+these link selection algorithms. We fix a fidelity gap = 0.05 according to the fidelity gap. Specifically, the smaller the
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1426on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+fidelity gap is, the harder to identify the optimal link, and
+therefore more resources are needed. When the fidelity gap
+is large, both L INK S EL F I E and SuccElimNB can identify the
+optimal link quickly. However, when the fidelity gap is small,
+benefiting from Lemma 1, L INK S EL F I E can obtain a much
+tighter confidence interval and eliminate inferior links faster,
+while SuccElimNB has to perform much more benchmarking
+subroutines to achieve sufficient confidence.
+
+(a) Depolarising Noise
+
+(b) Dephasing Noise
+
+(a) Depolarizing Noise
+
+(b) Dephasing Noise
+
+(c) Amplitude Damping Noise
+
+(d) Bit Flip Noise
+
+Fig. 5. Relative error v.s. the number of links L using different noise models.
+
+Vienna QKD network [28], SwissQuantum QKP network
+[29], Tokyo QKD network [30], and the space-to-ground
+network [28], demonstrating the promising potential of the
+upcoming quantum revolution. However, the susceptibility of
+quantum information to noise necessitates the characterization
+(c) Amplitude Damping Noise
+(d) Bit Flip Noise
+of quantum link noise for reliable quantum information transmission. Ruan [31] proposes a protocol to estimate the fidelity
+Fig. 4. Bounces v.s. gap using different noise models.
+of entanglement shared by remote nodes, but it does not take
+quantum measurement errors into account. Helsen et al. [20]
+C. Fidelity Estimation Accuracy
+propose a network benchmarking method, which is robust to
+Finally, we show the fidelity estimation accuracy of L INK - state preparation and measurement errors and can efficiently
+S EL F I E. We initialize a two-node network with L links, where and accurately estimate the fidelity of quantum links, regardless
+the fidelity of each link is generated as follows. We set of how these quantum links are formed. Recently, Andrade et
+µ1 = 0.95 and µi = 0.85 for i = 2, . . . , L, then for each al. [32] devise novel network tomography protocols (NTP) to
+link i, we sample its fidelity fi from a Gaussian distribution characterize the channel noise in quantum networks, but it only
+with mean µi and variance 1/4. We apply each algorithm to the considers bit-flip probabilities of quantum star networks. Liu et
+network, get the estimated fidelity of the identified optimal link, al. [33] propose quantum Border Gateway Protocol (BGP) to
+and calculate the relative error. Figure 5 plots the relative error support entanglement routing across multiple quantum Internet
+versus the number of links L, varying from 2 to 20, and the Service Providers (qISPs) and integrate network benchmarking
+results are averaged over 10 trials. As expected, L INK S EL F I E with the top-K arm identification problem. However, their
+can not only identify the optimal link but also evaluate its formulation has more stringent assumptions than ours. Our
+fidelity accurately. The relative error of L INK S EL F I E is less online link selection algorithm L INK S EL F I E leverages the
+than 1%, which has no significant difference compared with idea of online learning and inherits the favorable properties
+other algorithms. When the number of links is large, the relative of network benchmarking. When selecting the optimal link
+error tends to decrease because the algorithms need to spend from a set of links, L INK S EL F I E is much more efficient than
+more bounces to distinguish the optimal link, resulting in a network benchmarking.
+The multi-armed bandit (MAB) [34], [35] is a well-known
+more accurate estimation. In summary, L INK S EL F I E identifies
+the optimal link with significantly less quantum resource framework with numerous applications in various fields, such
+consumption while providing comparable fidelity estimation as crowdsensing [36], opportunistic channel access [37], and
+social networks [38]. In this literature, our model is related to
+accuracy.
+best arm identification with fixed confidence, aiming to identify
+VI. R ELATED W ORK
+the optimal arm with high probability using as few samples as
+Quantum networks have gained a lot of attention since their possible. To solve this problem, algorithms like the successive
+introduction. Several real-world quantum networks have been elimination algorithm [27], the lil’UCB algorithm [39], and
+successfully tested outside the laboratory, such as SECOQC the track-and-stop strategy [40] are proposed and theoretically
+
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1427on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+analyzed. The problem has also been extended to the best- measuring the survival probability at sequence length m 2 M.
+K arms identification setting [41], [42], with the objective to Since bmi is the average of T samples, the variance of its noise
+select top K arms with the highest means with high confidence. "i is 2 /T .
+The goal of non-linear least squares is to find the parameters
+Another variant of the best arm identification problem is to
+identify the best arm in the fixed-budget scenario [21], [43]– ✓b that minimize the sum of squares of residual errors S(✓),
+[45], which aims to minimize the probability of returning wrong where
+|M|
+X
+arms at the end of the time budget. We are the first to exploit the
+2
+S(✓)
+=
+(bmi f (mi ; ✓)) .
+MAB framework to solve the link selection and fidelity estimate
+i=1
+problem in quantum networks. Our algorithm deliberately
+We compute the confidence interval using the linear approxconsiders the property of the network benchmarking, with
+the objective of identifying the optimal high-fidelity link from imation method.
+Taking the Taylor expansion of function f (mi ; ✓) at point
+a link set with high confidence and consuming as few resources
+⇤
+✓
+= (A⇤ , p⇤ )T , we have
+as possible. Unlike using the standard confidence interval based
+on Hoeffding’s inequality to analyze the sample complexity
+@f (mi ; ✓)
+f (mi ; ✓) ⇡f (mi ; ✓ ⇤ ) +
+(A A⇤ )
+of algorithms in classical bandits, we deduce a confidence
+@A
+⇤
+✓
+interval for the network benchmarking subroutine and hereby
+@f (mi ; ✓)
+⇤
++
+(p p )
+analyze the cost complexity upper bound of our algorithm from
+(2)
+@p
+✓⇤
+a different perspective.
+2m
+=A⇤ (p⇤ ) i + (p⇤ )2mi (A A⇤ )
+VII. C ONCLUSION
+2m 1
++ 2mi A⇤ (p⇤ ) i (p p⇤ ) ,
+In this paper, we consider the problem of link selection
+and fidelity estimation in quantum networks. To address this where the ⇡ hides a small o(1) quantity.
+Hence,
+challenge, we formulate it as a best arm identification problem
+|M|
+and design an efficient algorithm named L INK S EL F I E. We
+X
+2
+S(✓) =
+(bmi f (mi ; ✓))
+derive a novel confidence interval of estimates for the vanilla
+i=1
+network benchmarking, a key subroutine within L INK S EL F I E,
+|M| ⇣
+and prove that given a confidence parameter 2 (0, 1), with the
+(a) X
+2m
+2m
+⇡
+bmi A⇤ (p⇤ ) i (p⇤ ) i (A A⇤ )
+probability of at least 1
+, L INK S EL F I E outputs the optimal
+(3)
+i=1
+link and its accurate estimate. We also prove a cost complexity
+⌘2
+2m
+1
+upper bound for L INK S EL F I E. To validate the performance of
+2mi A⇤ (p⇤ ) i (p p⇤ )
+L INK S EL F I E, we simulate a quantum network with quantum
+|M|
+X
+nodes connected via multiple entanglement links. Simulation
+2
+=
+"i (✓ ✓ ⇤ )T Fi ,
+results show that L INK S EL F I E outperforms other methods in
+i=1
+efficiently selecting the optimal link and accurately estimating
+f (mi ; ✓) with its Taylor expansion
+the fidelity while consuming fewer quantum resources across where (a) is by substituting
+⇣
+⌘T
+2m 1
+various scenarios.
+(2) above, and Fi = (p⇤ )2mi , 2mi A⇤ (p⇤ ) i
+and " =
+The authors have provided public access to their code and/or
+T
+("1 , . . . , "|M| ) .
+data at https://zenodo.org/doi/10.5281/zenodo.10444443.
+After the linear approximation, we can minimize (3) by the
+linear least squares and get:
+A PPENDIX
+0
+1 1
+|M|
+|M|
+A. Proof of Lemma 1
+X
+X
+⇤
+TA
+@
+(4)
+"i F i
+✓
+✓
+=
+F
+F
+i i
+Since the estimate fidelity p̂ is obtained by non-linear
+i=1
+i=1
+regression, we use the linear approximation method [46], [47]
+to derive the confidence interval of p̂ for the vanilla network
+Equation (4) shows that ✓ ✓ ⇤ is a linear combination of
+benchmarking.
+"i ⇠ N (0, 2 /T ). By the definition of multivariate normal
+In the model bm = Ap2m , ✓ = (A, p)T are the parameters distribution, we have
+✓
+◆
+we want to estimate. We denote their true values by ✓ ⇤ =
+2
+b pb)T .
+✓b ⇠ N2 ✓ ⇤ , Q ,
+(A⇤ , p⇤ )T , and their least-square estimates by ✓b = (A,
+T
+In network benchmarking, the observed data (mi , bmi ) for
+⇣P
+⌘ 1
+|M|
+i = 1, . . . , |M| are i.i.d. random samples drawn from the where Q =
+T
+.
+i=1 Fi Fi
+non-linear model as follows:
+Since we only care about the estimation of p⇤ , by the property
+of multivariate normal distribution, we can extract the second
+bmi = f (mi ; ✓) + "i = Ap2mi + "i ,
+b pb)T , which has the distribution:
+component of ✓b = (A,
+✓
+◆
+2
+where "i is the noise term, which follows the normal distribu⇤
+pb ⇠ N p , Q2,2 .
+tion N (0, 2 /T ). Parameter 2 is the single-shot variance for
+T
+Authorized licensed use limited to: Chinese University of Hong Kong. Downloaded
+1428on August 15,2024 at 02:47:32 UTC from IEEE Xplore. Restrictions apply.
+
+where Q2,2 is the entry of Q in the second row and the second
+column.
+Although Q2,2 depends on the true values A⇤ and p⇤ , which
+are unknown to us, the inherent range of A⇤ and p⇤ [22]
+shows that Q2,2 is bounded. We can approximate Fi using
+⇣
+⌘T
+⇣
+⌘ 1
+b = P|M| Fbi Fb T
+bp2mi 1
+Fbi = pb2mi , 2mi Ab
+and so Q
+.
+i=1
+
+Since
+Pr Ē 6
+6
+
+i
+
+We approximate the sample variance s2 as follows,
+s2 =
+
+b
+S(✓)
+|M| 2
+⇡
+.
+|M| 2
+(|M| 2)T
+
+Finally, we get the asymptotic confidence interval of p⇤ by
+the property of t-distribution as follows,
+s
+"
+#
+1
+|M|
+⇤
+b
+Pr |b
+p p |> p
+· Q2,2 · t|M| 2,1 ↵/2 6 ↵,
+|M| 2
+T
+
+where tk,p is the p-th quantiles of the t-distribution with k
+degrees of freedom. That is, the confidence interval depends
+on O( p1T ).
+Let
+|M|
+b 2,2 · t2
+C= 2
+·Q
+|M| 2,1 ↵/2
+|M| 2
+
+for a fixed value of ↵. By applying the powering lemma [48],
+i.e., repeating the algorithm O(log 1 ) times and taking the
+median, the vanilla network benchmarking method can return
+pb such that
+"
+#
+r
+C
+1
+⇤
+Pr |p̂ p | >
+log
+6 ,
+T
+
+Then we can conclude Lemma 1.
+
+Proof. We now prove Theorem 1 by showing that, with
+probability of at least 1
+, (a) the optimal link will always
+remain in the candidate set S, and (b) the number of pulls
+required for a suboptimal link i to be removed from S is
+bounded by O(C i 2 log (L/ log (4 i 1 ))).
+First, we prove (a): Note that link i will be eliminated from
+S only if there exists some j 6= i and some s > 0 such that
+(s)
+
+(s)
+
+2 s.
+
+(5)
+
+(s)
+
+We denote the event {8s > 0, 8i 2 S, |p̂i
+pi | 6 2 s } by
+(s)
+s (s)
+s
+E. On the event E, pi 2 [p̂i
+2 , p̂i + 2 ] holds for any
+(s)
+link i 2 S in any stage s > 0. and thus, p̂i + 2 s > pi and
+(s)
+s
+p̂j
+2 6 pj . Plugging them into (5), we have
+(s)
+
+(s)
+
+pi 6 p̂i + 2 s < p̂j
+
+⇣
+(s)
+Pr |p̂i
+
+s=1 i2S
+
+|S|s(s + 1)
+
+s=1 i2S
+1 X
+X
+
+2 s 6 pj ,
+
+showing that pi < pj , i.e., i is not an optimal link.
+Therefore, if the event E holds, Algorithm 1 never makes
+mistakes and must output the correct optimal link in the end.
+It is sufficient to show that the probability that the event E
+happens is no less than 1
+.
+
+pi | > 2 s
+
+⌘
+
+(6)
+(7)
+(8)
+
+< ,
+
+where (6) holds by
+the union bound, (7) is because of Lemma 1,
+P1
+1
+< 1, i.e., Pr(E) > 1
+and (8) is from s=1 s(s+1)
+, we can
+conclude (a).
+Then we prove (b): We consider the cost complexity when
+E holds. We show that a suboptimal link i must have been
+eliminated when i 6 4 · 2 s ; otherwise, it results in a
+contradiction. Suppose i > 4·2 s and link i is not eliminated
+(s)
+in phase s, implying that p̂i + 2 s > p̂max 2 s . Then,
+(s)
+
+(s)
+
+pi +2·2 s > p̂i +2 s > p̂max +2 s > p̂1
+
+2 s > p1 2·2 s ,
+
+holds, i.e., i 6 4 · 2 s , which contradicts with i > 4 · 2 s .
+Denote the phase in which link i is eliminated by phase si .
+We have i 6 4 · 2 si . Therefore, the total number of pulls
+of link i is upper bounded as follows,
+Ni,si = C22si log
+
+si (si + 1)|S|
+
+6 C22si log
+
+si (si + 1)L
+
+(9)
+
+✓
+
+L
+4
+4
+6 C22si log
+log
+(log
++ 1)
+i
+✓
+✓
+◆◆ i
+C
+L
+4
+=O
+log
+,
+2 log
+
+◆
+
+(10)
+(11)
+(12)
+
+i
+
+i
+
+B. Proof of Theorem 1
+
+p̂i + 2 s < p̂j
+
+1 X
+X
+
+where (9) is from the definition, (10) is because of |S| 6 L,
+(11) and (12) are because of i 6 4 · 2 si . Then we have (b).
+Summing over the number of pulls of all links and multiplying it with the cost per pull, we have:
+✓
+◆! X
+X C
+L
+4
+Cost(AL INK S EL F I E ) 6 O
+log
+·
+m,
+2 log
+i2L
+
+i
+
+i
+
+m2M
+
+which concludes the proof.
+
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+
+
+
+この論文「**LINK SELFIE: Link Selection and Fidelity Estimation in Quantum Networks**」（IEEE INFOCOM 2024）が解いている問題の**入力、出力、制約条件、目的関数**は以下のように整理できます。
+
+---
+
+### 🔶【問題の概要】
+
+量子ネットワークにおいて、**複数の量子リンク（エンタングルメントリンク）**の中から、**最も忠実度（fidelity）が高いリンクを選択**し、その**忠実度を高精度に推定**したい。
+ただし、忠実度は事前には不明で、すべてのリンクを均等に評価するにはコスト（量子リソース消費）が高すぎる。
+
+---
+
+## 🔹1. 入力（Input）
+
+ * `L = {l₁, l₂, ..., l_L}`：
+  ソースノードSとデスティネーションノードDを結ぶ **L本のエンタングルメントリンク**の集合。それぞれのリンク `lᵢ` は不明な忠実度 `fᵢ ∈ [0, 1]` を持つ。
+
+ * `M = {m₁, m₂, ..., m_M}`：
+  **バウンス回数**（リンクを何回往復させるか）の集合。
+
+ * `T`：
+  各バウンス回数ごとの**繰り返し回数（実験回数）**。
+
+ * `δ ∈ (0, 1)`：
+  信頼度（たとえば95%信頼区間などに相当）。
+
+---
+
+## 🔹2. 出力（Output）
+
+ * `l*`：
+  最も忠実度が高いと判断されたリンク `l* ∈ L`
+
+ * `f̂*`：
+  選ばれたリンク `l*` の**推定忠実度**。誤差は高確率で小さい。
+
+---
+
+## 🔹3. 制約条件（Constraints）
+
+ * **未知の忠実度**：
+  各リンクの忠実度 `fᵢ` は事前にわからず、ネットワークベンチマーク（qubitを何度も送る）によって推定する必要がある。
+
+ * **リソース制限**：
+  各リンクの評価には\*\*量子リソース（エンタングルメント消費、バウンス数）\*\*がかかる。全リンクを同程度に調査することは非効率。
+
+ * **精度要件**：
+  忠実度の推定誤差 `|f̂ᵢ - fᵢ| < ε` かつ、全体として `1 - δ` の確率で正しい最適リンクを選出することが求められる。
+
+---
+
+## 🔹4. 目的関数（Objective Function）
+
+### **目的：**
+
+最小のコストで、最も忠実度が高いリンク `l*` を見つけ、その忠実度 `f*` を高精度に推定する。
+
+### **数式表現：**
+
+```math
+\min \text{Cost}(A) = \sum_{i \in L} \sum_{m \in M} N_{i,m} \cdot m
+```
+
+ここで、
+
+ * `N_{i,m}` はリンク `i` に対してバウンス数 `m` を用いてネットワークベンチマークを行った回数。
+ * `m` は1回の実験あたりの消費リソース。
+
+---
+
+## 🔸補足（手法の概要）
+
+ * 問題は「**多腕バンディットにおけるベストアーム識別問題（Best Arm Identification, BAI）**」として定式化されている。
+ * 提案手法 **LINK SELFIE** は、信頼区間ベースで劣ったリンクを早期に削除し、必要なリンクにだけリソースを集中させる。
+ * ネットワークベンチマーク結果に対して、非線形回帰（指数モデル）を適用して忠実度を推定。
+ * コスト（量子リソース消費）に理論的な上限を設け、他の手法より効率が良いことを証明。
+
+---
+
+ご希望であれば、数式付きのLaTeX形式や、ベストアーム識別問題と従来手法との比較表も作成できます。
+
+** Q. LinkSelfie の論文の問題を拡張したい。
+以下のように拡張した問題の入力、出力、制約条件、目的関数を説明して。
+ノードS〜ノードD 間のリンク集合 Ｌ だけでなく、
+ノードS〜ノードD_n間のリンク集合 L_n (1 <= n <= N, N はノードSの隣接ノード数)がそれぞれ入力される。
+ノードS〜ノードD_n間の重要度 I_n (0〜1 の値) が入力として与えられる。
+総バウンスコスト C が入力として与えられる。
+この時、ノードS〜ノードD_n のノードペアの中で、
+K 個のノードペア (S, D_s_1), (S, D_s_2), ... (S, D_s_K) における
+忠実度が最大のリンクをそれぞれ発見する。
+ただし、発見するリンクのノードペア数 K は、
+重要度と忠実度の積の総和、つまり
+I = \sum_{k = 1}^K I_s_k * F_s_k 
+が最大となるように定める。
+ここで F_n は (S, D_n) 間において忠実度の最大のリンクの忠実度である。
+
+A. この拡張問題は、複数のノードペア (S, Dₙ) に対して、限られたリソース（バウンスコスト）の中で、重要なノードペアの
+高忠実度リンクを選定する最適化問題です。以下に、この問題の形式的な定義を記述します。
+
+🔶 問題名（例）：
+
+Weighted Multi-Pair Link Selection and Fidelity Estimation under Cost Constraint
+
+🔷 1. 入力（Input）
+
+🔸 ネットワーク構成
+- N ∈ ℕ⁺：
+ ソースノード S に接続している隣接ノードの数（= ノードペア数）
+- Lₙ = {lₙ₁, ..., lₙ_Lₙ}：
+ 各ノードペア (S, Dₙ) における量子リンク集合。各リンク lₙⱼ は未知の忠実度 fₙⱼ ∈ [0,1] を持つ。
+
+🔸 メタ情報
+- Iₙ ∈ [0, 1]：
+ ノードペア (S, Dₙ) の重要度（重み）
+- C ∈ ℝ⁺：
+ 使用できる総バウンスコスト（＝量子リソース上限）
+
+🔷 2. 出力（Output）
+- ノードペア選定集合 S_sel = {n₁, n₂, ..., n_K}（|S_sel| = K）
+- 各選ばれたノードペア nₖ ∈ S_sel に対して、
+ 最大忠実度リンク lₙₖ* ∈ Lₙₖ とその推定忠実度 f̂ₙₖ*
+
+🔷 3. 制約条件（Constraints）
+1 バウンスコスト制約：
+ - 評価にかかった総バウンスコストの合計が C を超えてはならない
+ - すなわち、
+
+ ∑n=1N∑l∈LnCostn(l)≤C∑_{n=1}^N ∑_{l ∈ Lₙ} Cost_n(l) ≤ C n=1∑N​l∈Ln​∑​Costn​(l)≤C 
+
+ ※Cost_n(l) はそのリンクにおけるベンチマークのバウンス数（＝リンク評価コスト）
+2 忠実度は未知：
+ - 各リンク lₙⱼ の忠実度 fₙⱼ は、ネットワークベンチマーク（複数回バウンス）を通じて推定される
+3 忠実度推定精度（信頼性）：
+ - 各推定値 f̂ₙⱼ は、ある信頼度1−δで正確性が保証される
+
+🔷 4. 目的関数（Objective Function）
+
+選んだ K 個のノードペア (S, Dₙₖ) に対して、
+各ペア内で最良リンク lₙₖ* を選び、以下の価値関数を最大化する：
+
+Itotal=∑k=1KInk∗F^nkI_total = ∑_{k=1}^K I_{n_k} * F̂_{n_k} It​otal=k=1∑K​Ink​​∗F^nk​​ 
+
+ここで：
+- I_{n_k} はノードペアの重要度
+- F̂_{n_k} はそのノードペア内の最良リンクの推定忠実度
+
+🔷 要約（形式的な最適化問題）
+
+mathematica
+SVG ImageCopySVG ImageEdit
+最大化：
+    I_total = ∑_{n ∈ S_sel} I_n * F̂_n*
+
+制約：
+    ∑_{n=1}^N ∑_{l ∈ L_n} BenchmarkCost(l) ≤ C
+    S_sel ⊆ {1, 2, ..., N}, |S_sel| = K（K は自動で決まる）
+
+🔸 この拡張の本質的なポイント
+- 単一リンク選定（元のLinkSelfie） → 複数ペア×リンクの選定（マルチリンク・マルチペア問題）
+- 静的な目標（忠実度最大） → 動的な目標（重要度×忠実度最大）
+- 固定K → Kは結果に応じて最適に変化
+
+🔸 解法に向けた示唆（発展）
+
+この問題は以下を融合したリソース制約付きの最適ペア・リンク探索問題として捉えられます：
+- BAI（Best Arm Identification）× 多目的最適化
+- 重要度付き knapsack + adaptive sampling
+- 各ペアで局所的に BAI をしつつ、ペア間で 重要度×見込み忠実度の期待値を最大化するように選定
+
+必要であれば、これを実装可能な擬似コード設計や、アルゴリズム構成（段階的フェーズスケジューリング）の提案にも進め
+られます。どうされますか？
+** Q. Weighted Multi-Pair Link Selection and Fidelity Estimation under Cost Constraint 問題の、
+比較的単純で、なおかつ良好な解が得られると期待されるアルゴリズムを示して。
+アルゴリズムの実行例も示して
+
+A. 以下に、あなたの定義した 「Weighted Multi-Pair Link Selection and Fidelity Estimation under Cost
+Constraint」 に対して、
+- 比較的単純
+- 実用的に良好な解が期待できる
+- 逐次的で実装容易なアルゴリズム
+
+を提案し、実行例（手計算ベース）も示します。
+
+✅ アルゴリズム案：
+
+Greedy Pairwise BAI with Budget-Aware Scheduling
+
+🔸 アイデア概要
+1 各ノードペア (S, Dₙ) ごとに「少しだけ」リンク評価を行い、最良リンクの推定忠実度 f̂ₙ を取得
+2 それを基に、Iₙ × f̂ₙ が高い順に並べ、価値効率の良いノードペアから順に精密評価
+3 コスト C を超えない範囲で、BAIにより最良リンクを選定していく
+
+🔸 擬似コード
+
+python
+SVG ImageCopySVG ImageEdit
+Input: 
+  - ノードペア集合 {D₁, ..., D_N}
+  - 各ペアのリンク集合 Lₙ と重要度 Iₙ
+  - バウンスコスト予算 C
+  - 初期評価回数 T₀, 信頼度 δ
+
+Step 1: 初期推定（各ノードペアにT₀回ずつ均等評価）
+  for each n in 1..N:
+      for each link l in Lₙ:
+          evaluate link l using T₀回ベンチマーク → 推定忠実度 f̂ₙₗ
+      Let l*ₙ = argmax_l f̂ₙₗ
+      Set f̂ₙ = f̂ₙₗ* （最良リンクの忠実度）
+      Compute 価値スコア vₙ = Iₙ × f̂ₙ
+
+Step 2: 優先度順にペアを並び替え
+  Sort all pairs by vₙ in descending order → Q = [(n₁,v₁), (n₂,v₂), ...]
+
+Step 3: 各ペアに本格BAI実行（予算を消費）
+  RemainingCost = C - InitialCost
+  Result = []
+
+  for (n, v) in Q:
+      Estimate cost_required for BAI(n)
+      if cost_required <= RemainingCost:
+          Run BAI to find best link in Lₙ → f̂ₙ*
+          Append (n, f̂ₙ*, Iₙ) to Result
+          RemainingCost -= cost_required
+      else:
+          break
+
+Output:
+  - 選ばれたノードペア集合と各最良リンクの忠実度
+  - 最大化された I_total = Σ Iₙ × f̂ₙ*
+
+✅ 実行例
+
+🔸 前提
+
+  n（ノードペア）  Iₙ（重要度）  リンク候補（忠実度）    
+  1  0.9  [0.85, 0.80]    
+  2  0.5  [0.70, 0.75, 0.60]    
+  3  0.8  [0.60, 0.58]    
+  4  0.3  [0.95, 0.90]    
+- コスト予算 C = 80 バウンス
+- 初期評価回数 T₀ = 5 per link
+ → 初期コスト = (2+3+2+2) × 5 = 45 バウンス消費
+
+🔸 Step 1：初期推定
+
+  n  最良リンク f̂ₙ  vₙ = Iₙ × f̂ₙ    
+  1  0.85  0.765    
+  2  0.75  0.375    
+  3  0.60  0.480    
+  4  0.95  0.285    
+
+🔸 Step 2：並べ替え（価値順）
+
+順序：1 → 3 → 2 → 4
+
+🔸 Step 3：順次BAI
+
+・ノードペア1にBAI（仮に 20 バウンス消費）
+
+→ f̂₁* = 0.86（高精度推定）
+
+・ノードペア3にBAI（仮に 10 バウンス）
+
+→ f̂₃* = 0.62
+
+→ 残コスト：80 − 45 − 20 − 10 = 5（終了）
+
+🔸 出力結果
+
+選ばれたペア：n=1, n=3
+忠実度と重要度：
+- (1) I₁ × f̂₁* = 0.9 × 0.86 = 0.774
+- (3) I₃ × f̂₃* = 0.8 × 0.62 = 0.496
+
+→ 合計目的関数値（I_total） = 1.270
+
+✅ 特徴・評価
+
+  項目  内容    
+  長所  単純で実装容易、初期評価に基づく有望ペアの優先選定    
+  短所  初期評価が粗すぎると誤った選定に陥る可能性あり    
+  改善案  初期ステージを adaptively 決める or BAIの一部予測    
+
+ご希望であれば、これを Pythonコード化したものや、BAIのアルゴリズム部分の統合, より効率的な選定戦略（例：価値密
+度Iₙ×fₙ/コスト）による拡張版も提供可能です。希望されますか？
+** 
+Q. 共通リソースからとってきているが、リソースはリンクに対してわりあてられている
+A. ネットワークを運用している人のお金の問題で決まる、GAFA がやるなら、バウンスをたくさん用意できるだろうし…。
+
+
+
+
+段落の一文目をトピックセンテンスとして、段落の主旨を明確にして。
+各トピックセンテンスだけを読んで、論文の論旨が理解できるように書いて。
+論理が飛躍している箇所は適宜補って。
+説明が不足している箇所は説明を追加して。
+情報科学分野の学術論文にふさわしい内容にして。
+大崎博之氏の文体にできるだけ近づけて。大崎博之氏の論文の PDF ファイルは以下から入手できる。https://lsnl.jp/~ohsaki/papers/list-workshop.html
+
+
+
+
+
+
+
+--- 以下の論文を以下の章構成にリライトして。
+1. はじめに 背景 量子ネットワークにおいて忠実度を高いリンクを効率的に判定する手法 LinkSelFiE が提案されている
+動機 LinkSelFiE は通信需要を考慮していないが、現実には通信需要が高くかつ忠実度の高いリンクの判定が望まれる
+目的 少ない計測 (バウンス) により利用率 x 忠実度が高いリンクの判定を可能とする
+2. 量子ネットワークにおけるリンク忠実度計測問題を、通信需要を重
+み付け要素として組み込む形で定式化する入力、出力、制約条件、目的関
+   数
+3. 提案手法の説明
+4. 実験の目的、実験の条件、結果、考察
+5. まとめと今後の課題
+だ・である調で書いて。「まとめと今後の課題」以外の章は、それぞれ 4 段
+落に増やして、各段落は 200 文字程度にして。段落の一文目をトピックセン
+テンスとして、段落の主旨を明確にして。各トピックセンテンスだけを読んで、
+論文の論旨が理解できるように書いて。論理が飛躍している箇所は適宜補って。
+説明が不足している箇所は説明を追加して。情報科学分野の学術論文にふさわ
+しい内容にして。日本語の文体は、大崎博之氏の文体にできるだけ近づけて。
+大崎博之氏の論文の PDF ファイルは以下から入手できる。
+https://lsnl.jp/~ohsaki/papers/list-workshop.html
+
+
+--- [全文]
+
+
+
+7月中にどこまで進めるか
+8月1日までに
+ある程度のスライド完成
+
+だれ向けにスライドをつくるか
+インターネットアーキテクチャの分野
+なにを知らないか考える
+学生とかも聞きにくる
+分からない人向けに説明する
+量子ネットワークを分からない人もくる
+
+'何を話したいか'から考える
+だれに何を伝えたいか
+卒研とソサイエティでは内容が異なる
+
+アプローチは正しい
+
+25までにスライドのコンパイルをできるようにする
+orgモードからつくってコンパイルできるようにする
+
+
+29までにyutoさんにみてもらう
+29はおそい
+
+1回目の発表練習にどの程度のものを準備するか
+全員に意見がくる
+1回目に完璧はもとめられてない
+
+
+yutoさんとスケジュールをきめる
+yutoさんの力をどう借りるか
+共著の先輩方のリソースをどう使うか
+
+スライドつくるときは各スライドで何を伝えたいか(主張)決める
+スライドの何枚にするのかを最初に決める
+ここを相談する。骨格の部分を相談する
+
+何枚の構成か
+それぞれのスライドで何を伝えるのか
+骨格を
+
+
+
+
+
+ソサイエティの発表までに
+何かやっとくといい
+ソサイエティの内容から発展した結果を得られるようにする
+
+研究は複数枚の原稿になる
+国際会議のフィードバックを打診する
+雑誌までいけたらいく
+
+卒研の発表は自分でやったことを説明する
+
+
+国際会議のどこに出したいか
+geminiやgptでしらべる
+infocom,icc,compsac
+
+すぐcompsacはきつい
+iccなど6ページの学会にだす
+量子ネットワーク専門の学会があるかも
+
+iccのフィードバックをもとに出すのがいい
+
+
+中身
+なにをするか
+ここから進化させるためには
+
+同じ内容で6ページかいてみる
+
+貪欲法をかえる
+新しい手法の提案
+ニーズがあってそれに答えるような手法が必要
+手法を変えることにどういう意味があるのか
+
+inputを増やす
+手を動かすのと同時並行でおこなう
+すぐできる実験を動かしたりする
+今すぐ論文をかくのが大事(今の論文を6ページにするならどうするか)
+
+input3
+手をうごかす4
+考える3
+
+
+何を明らかにしているか
+測定資源を減らす
+
+この研究で何をしたいか
+自分の研究が何をする研究なのかを定める
+ソサイエティのときのストーリーを大事にする
+これをもとに他の研究は何をしているか、実験はこれでいいのかを考える
+どういう実験でどういうスコアを出したらいいのかなど
+
+
+
+次回
+木曜3限以外
+時間セットで候補3つくらい30ー1時間くらい
+
+yutoさんとうまくやる
+研究も
+yutoさんと話したあとshotaさんとはなす
+shotaさんとyutoさんはセットで
+
+分担orブラッシュアップ
+

rangecite.sty

@@ -0,0 +1,92 @@
+%From: reingold@emr.cs.uiuc.edu (Edward M. Reingold)
+%Newsgroups: comp.text.tex
+%Subject: Re: short form references like [1-4]
+%Date: 26 Mar 91 22:44:32 GMT
+%Organization: University of Illinois at Urbana-Champaign
+%
+%In article <880@imec.UUCP> symons@imec.be (Jan Symons) writes:
+%
+%   with LaTeX, the \cite{key1,key2,key3,key4} puts a [1,2,3,4] reference
+%   in the text. However, what I want to see is more like [1-4].
+%
+%   Can somebody please explain how this can be achieved with LaTeX ?
+%
+%
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+% 
+% Nachum Dershowitz (nachum@cs.uiuc.edu)
+% Edward M. Reingold (reingold@cs.uiuc.edu)
+%
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+         \setcounter{@@@cur}{\value{@@@next}}%
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slide.org

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+# -*- Org -*-
+#
+# Copyright (c) 2010, Hiroyuki Ohsaki.
+# All rights reserved.
+#
+# $Id: 120111-impact.org,v 1.1 2012/01/12 02:56:04 oosaki Exp oosaki $
+#
+
+#+STARTUP: beamer
+#+LATEX_CLASS: beamer
+#+LATEX_CLASS_OPTIONS: [compress,dvipdfm,12pt]
+#+OPTIONS:    toc:nil
+#+BEAMER_FRAME_LEVEL: 2
+#+BEAMER_HEADER_EXTRA: \usetheme{Ohsaki}
+#+BEAMER_HEADER_EXTRA: \usepackage{palatino}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\sfdefault}{ppl}
+#+BEAMER_HEADER_EXTRA: \title[Fidelity Measurement Considering Demand]{通信需要を考慮した量子ネットワークのリンク忠実度計測手法に関する一検討}
+#+BEAMER_HEADER_EXTRA: \author[S. Yamachika et al.]{山近 駿\inst{1}、柿原 悠人\inst{2}、井上 翔太\inst{2}、大崎 博之\inst{2}}
+#+BEAMER_HEADER_EXTRA: \institute{\inst{1} 関西学院大学 工学部 \and \inst{2} 関西学院大学 大学院理工学部研究科}
+#+BEAMER_HEADER_EXTRA: \date{2025年7月20日}
+#+BEAMER_HEADER_EXTRA: \setlength{\parskip}{1.5ex}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\textbf}{\alert}
+
+* 背景
+- 量子ネットワークでは、環境ノイズの影響を受けやすいため、高信頼な通信には**忠実度の高い量子リンク**の選択が不可欠。
+- しかし、リンクの忠実度を正確に推定するには**多大な測定コスト**（時間や量子ビット）を要する。
+- 限られた測定資源をいかに効率的に配分するかが重要な課題となっている。
+
+* 動機
+p- 既存のリンク忠実度特定手法（LinkSelFiEなど）は、**各通信経路の重要度（通信需要）を考慮していない**。
+- すべてのリンク候補を同等に扱うため、通信需要に応じて測定資源を最適に配分できない。
+- 重要な通信経路の品質を優先的に保証する方が、ネットワーク全体としての価値は高まるはず。
+
+* 目的
+- 通信需要を**定量的な重み**として導入し、限られた測定資源をリンクの価値に応じて最適に配分する新たな手法を提案する。
+  - 各通信経路の重要度と忠実度の積をその経路の**価値**と定義。
+  - ネットワーク全体の**総価値を最大化**する問題として定式化する。
+  - 上記問題に対し、効率的な準最適解法として**二段階貪欲法**を提案し、その有効性を評価する。
+
+* 問題定義：通信需要を考慮したリンク忠実度計測問題
+- **入力**
+  - ノードペア集合 $(S, D_n)$、各ペアの並列リンク集合 $L_n$
+  - 各ノードペアの**重要度** $I_n$
+  - **総測定予算** $C$
+- **目的**: ネットワーク全体の**総価値**を最大化する。
+  - 目的関数: $\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}$
+    ($S_{sel}$は選択されたノードペア集合、$\hat{F}^*_{n_k}$は最高と推定された忠実度)
+- **制約条件**
+  - 総測定コストが総測定予算 $C$ を超えないこと。
+  - $\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C$
+
+* 提案手法：二段階貪欲法 (Two-Phase Greedy)
+- 広域的な探索と集中的な活用を組み合わせ、限られた測定資源を効率的に配分する。
+- **第一段階：広域探索フェーズ**
+  - 測定予算の一部を全リンクに少量ずつ均等に配分。
+  - 全リンクの忠実度の**初期推定値**を低コストで得る。
+- **第二段階：活用フェーズ**
+  - **価値スコア** ($= \text{重要度} \times \text{初期推定忠実度}$) を算出。
+  - スコアが高い有望なノードペア内のリンク群に、残りの測定資源を集中的に投下 (LinkSelFiEを適用)。
+
+* 実験の目的
+- 提案手法が、限られた測定予算のもとで**ネットワーク全体の総価値**を効率的に最大化できることをシミュレーションにより定量的に示す。
+
+* 実験シナリオ
+- **シミュレータ**: NetSquid
+- **トポロジ**: スター型 ($N=3$ および $N=5$)
+  - 各ノードペア間に5本の並列リンクが存在。
+- **忠実度設定**: 平均0.95のリンク1本、平均0.85のリンク4本（正規分布）
+- **重要度** $I_n$: 区間 $[0, 1]$ の一様乱数
+- **評価指標**: ネットワーク総価値スコア
+- **試行回数**: 各設定で20回実施し、平均値と95%信頼区間を算出。
+
+* 比較手法
+- **提案手法 (Two-Phase Greedy)**
+  - 価値スコアに基づき、有望なノードペアに資源を集中配分する。
+- **Uniform-LinkSelFiE**
+  - 全てのノードペアに測定予算を**均等配分**し、各ペア内でLinkSelFiEを適用する。
+- **Uniform-Naive**
+  - 全てのリンクに測定予算を**均等配分**する。
+
+* 測定予算と総価値スコアの関係
+#+ATTR_LATEX: :width 0.9\textwidth
+- [[./graphA.eps]] [[./graphC.eps]]
+- **考察1**
+  - 全ての測定予算条件において、**提案手法が比較手法よりも高い総価値スコアを達成**した。
+  - これは、通信需要と初期推定品質に基づき、価値の高いリンクへ優先的に資源を配分する戦略の有効性を示している。
+- **考察2**
+  - ノード数が増加すると（$N=3 \to 5$）、**提案手法と比較手法との性能差がより拡大**した。
+  - 探索対象が増え資源制約が厳しくなる大規模な状況ほど、提案手法の優位性が際立つことを示唆している。
+
+* まとめと今後の課題
+#+ATTR_LATEX: :options [t]
+#+begin_columns
+#+begin_column: .5\textwidth
+** まとめ
+- 通信需要を考慮したリンク忠実度計測問題を定義し、その準最適解法として**二段階貪欲法**を提案した。
+- シミュレーション評価により、提案手法が比較手法よりも効率的にネットワーク全体の総価値を高めること、特に**大規模で資源制約が厳しいネットワークにおいて有効**であることを示した。
+#+end_column
+#+begin_column: .5\textwidth
+** 今後の課題
+- 実際の量子ネットワークで用いられる、より**複雑なトポロジ**における有効性の検証。
+- 通信需要が時間的に変動する**動的な環境**へのアルゴリズムの適応。
+- 測定コストだけでなく、他のリソース（エンタングルメント生成時間など）も考慮した多目的最適化。
+#+end_column
+#+end_columns

slide.org~

@@ -0,0 +1,105 @@
+# -*- Org -*-
+#
+# Copyright (c) 2010, Hiroyuki Ohsaki.
+# All rights reserved.
+#
+# $Id: 120111-impact.org,v 1.1 2012/01/12 02:56:04 oosaki Exp oosaki $
+#
+
+#+STARTUP: beamer
+#+LATEX_CLASS: beamer
+#+LATEX_CLASS_OPTIONS: [compress,dvipdfm,12pt]
+#+OPTIONS:    toc:nil
+#+BEAMER_FRAME_LEVEL: 2
+#+BEAMER_HEADER_EXTRA: \usetheme{Ohsaki}
+#+BEAMER_HEADER_EXTRA: \usepackage{palatino}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\sfdefault}{ppl}
+#+BEAMER_HEADER_EXTRA: \title[Fidelity Measurement Considering Demand]{通信需要を考慮した量子ネットワークのリンク忠実度計測手法に関する一検討}
+#+BEAMER_HEADER_EXTRA: \author[S. Yamachika et al.]{山近 駿\inst{1}、柿原 悠人\inst{2}、井上 翔太\inst{2}、大崎 博之\inst{2}}
+#+BEAMER_HEADER_EXTRA: \institute{\inst{1} 関西学院大学 工学部 \and \inst{2} 関西学院大学 大学院理工学部研究科}
+#+BEAMER_HEADER_EXTRA: \date{2025年7月20日}
+#+BEAMER_HEADER_EXTRA: \setlength{\parskip}{1.5ex}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\textbf}{\alert}
+
+* 背景
+- 量子ネットワークでは、環境ノイズの影響を受けやすいため、高信頼な通信には**忠実度の高い量子リンク**の選択が不可欠。
+- しかし、リンクの忠実度を正確に推定するには**多大な測定コスト**（時間や量子ビット）を要する。
+- 限られた測定資源をいかに効率的に配分するかが重要な課題となっている。
+
+* 動機
+- 既存のリンク忠実度特定手法（LinkSelFiEなど）は、**各通信経路の重要度（通信需要）を考慮していない**。
+- すべてのリンク候補を同等に扱うため、通信需要に応じて測定資源を最適に配分できない。
+- 重要な通信経路の品質を優先的に保証する方が、ネットワーク全体としての価値は高まるはず。
+
+* 目的
+- 通信需要を**定量的な重み**として導入し、限られた測定資源をリンクの価値に応じて最適に配分する新たな手法を提案する。
+  - 各通信経路の重要度と忠実度の積をその経路の**価値**と定義。
+  - ネットワーク全体の**総価値を最大化**する問題として定式化する。
+  - 上記問題に対し、効率的な準最適解法として**二段階貪欲法**を提案し、その有効性を評価する。
+
+* 問題定義：通信需要を考慮したリンク忠実度計測問題
+- **入力**
+  - ノードペア集合 $(S, D_n)$、各ペアの並列リンク集合 $L_n$
+  - 各ノードペアの**重要度** $I_n$
+  - **総測定予算** $C$
+- **目的**: ネットワーク全体の**総価値**を最大化する。
+  - 目的関数: $\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}$
+    ($S_{sel}$は選択されたノードペア集合、$\hat{F}^*_{n_k}$は最高と推定された忠実度)
+- **制約条件**
+  - 総測定コストが総測定予算 $C$ を超えないこと。
+  - $\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C$
+
+* 提案手法：二段階貪欲法 (Two-Phase Greedy)
+- 広域的な探索と集中的な活用を組み合わせ、限られた測定資源を効率的に配分する。
+- **第一段階：広域探索フェーズ**
+  - 測定予算の一部を全リンクに少量ずつ均等に配分。
+  - 全リンクの忠実度の**初期推定値**を低コストで得る。
+- **第二段階：活用フェーズ**
+  - **価値スコア** ($= \text{重要度} \times \text{初期推定忠実度}$) を算出。
+  - スコアが高い有望なノードペア内のリンク群に、残りの測定資源を集中的に投下 (LinkSelFiEを適用)。
+
+* 実験の目的
+- 提案手法が、限られた測定予算のもとで**ネットワーク全体の総価値**を効率的に最大化できることをシミュレーションにより定量的に示す。
+
+* 実験シナリオ
+- **シミュレータ**: NetSquid
+- **トポロジ**: スター型 ($N=3$ および $N=5$)
+  - 各ノードペア間に5本の並列リンクが存在。
+- **忠実度設定**: 平均0.95のリンク1本、平均0.85のリンク4本（正規分布）
+- **重要度** $I_n$: 区間 $[0, 1]$ の一様乱数
+- **評価指標**: ネットワーク総価値スコア
+- **試行回数**: 各設定で20回実施し、平均値と95%信頼区間を算出。
+
+* 比較手法
+- **提案手法 (Two-Phase Greedy)**
+  - 価値スコアに基づき、有望なノードペアに資源を集中配分する。
+- **Uniform-LinkSelFiE**
+  - 全てのノードペアに測定予算を**均等配分**し、各ペア内でLinkSelFiEを適用する。
+- **Uniform-Naive**
+  - 全てのリンクに測定予算を**均等配分**する。
+
+* 測定予算と総価値スコアの関係
+#+ATTR_LATEX: :width 0.9\textwidth
+- [[./graphA.eps]] [[./graphC.eps]]
+- **考察1**
+  - 全ての測定予算条件において、**提案手法が比較手法よりも高い総価値スコアを達成**した。
+  - これは、通信需要と初期推定品質に基づき、価値の高いリンクへ優先的に資源を配分する戦略の有効性を示している。
+- **考察2**
+  - ノード数が増加すると（$N=3 \to 5$）、**提案手法と比較手法との性能差がより拡大**した。
+  - 探索対象が増え資源制約が厳しくなる大規模な状況ほど、提案手法の優位性が際立つことを示唆している。
+
+* まとめと今後の課題
+#+ATTR_LATEX: :options [t]
+#+begin_columns
+#+begin_column: .5\textwidth
+** まとめ
+- 通信需要を考慮したリンク忠実度計測問題を定義し、その準最適解法として**二段階貪欲法**を提案した。
+- シミュレーション評価により、提案手法が比較手法よりも効率的にネットワーク全体の総価値を高めること、特に**大規模で資源制約が厳しいネットワークにおいて有効**であることを示した。
+#+end_column
+#+begin_column: .5\textwidth
+** 今後の課題
+- 実際の量子ネットワークで用いられる、より**複雑なトポロジ**における有効性の検証。
+- 通信需要が時間的に変動する**動的な環境**へのアルゴリズムの適応。
+- 測定コストだけでなく、他のリソース（エンタングルメント生成時間など）も考慮した多目的最適化。
+#+end_column
+#+end_columns

slide.snm

@@ -0,0 +1,20 @@
+\beamer@slide {sec:org02e75dd<1>}{1}
+\beamer@slide {sec:org02e75dd}{1}
+\beamer@slide {sec:orgf650a9d<1>}{2}
+\beamer@slide {sec:orgf650a9d}{2}
+\beamer@slide {sec:org61970c3<1>}{3}
+\beamer@slide {sec:org61970c3}{3}
+\beamer@slide {sec:orga8b260b<1>}{4}
+\beamer@slide {sec:orga8b260b}{4}
+\beamer@slide {sec:org3f84c05<1>}{5}
+\beamer@slide {sec:org3f84c05}{5}
+\beamer@slide {sec:org8e8e072<1>}{6}
+\beamer@slide {sec:org8e8e072}{6}
+\beamer@slide {sec:org6ff6669<1>}{7}
+\beamer@slide {sec:org6ff6669}{7}
+\beamer@slide {sec:orgd0082d1<1>}{8}
+\beamer@slide {sec:orgd0082d1}{8}
+\beamer@slide {sec:org020e8c0<1>}{9}
+\beamer@slide {sec:org020e8c0}{9}
+\beamer@slide {sec:orga40ae09<1>}{10}
+\beamer@slide {sec:orga40ae09}{10}

slide.tex

@@ -0,0 +1,171 @@
+% Created 2025-07-20 Sun 21:21
+% Intended LaTeX compiler: pdflatex
+\documentclass[compress,dvipdfm,12pt]{beamer}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usetheme{default}
+\author{shun}
+\date{\today}
+\title{}
+\hypersetup{
+ pdfauthor={shun},
+ pdftitle={},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 28.2 (Org mode 9.5.5)}, 
+ pdflang={English}}
+\begin{document}
+
+
+\begin{frame}[label={sec:orgf38ad61}]{背景}
+\begin{itemize}
+\item 量子ネットワークでは、環境ノイズの影響を受けやすいため、高信頼な通信には**忠実度の高い量子リンク**の選択が不可欠。
+\item しかし、リンクの忠実度を正確に推定するには**多大な測定コスト**（時間や量子ビット）を要する。
+\item 限られた測定資源をいかに効率的に配分するかが重要な課題となっている。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orgee160e3}]{動機}
+\begin{itemize}
+\item 既存のリンク忠実度特定手法（LinkSelFiEなど）は、**各通信経路の重要度（通信需要）を考慮していない**。
+\item すべてのリンク候補を同等に扱うため、通信需要に応じて測定資源を最適に配分できない。
+\item 重要な通信経路の品質を優先的に保証する方が、ネットワーク全体としての価値は高まるはず。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org8672cac}]{目的}
+\begin{itemize}
+\item 通信需要を**定量的な重み**として導入し、限られた測定資源をリンクの価値に応じて最適に配分する新たな手法を提案する。
+\begin{itemize}
+\item 各通信経路の重要度と忠実度の積をその経路の**価値**と定義。
+\item ネットワーク全体の**総価値を最大化**する問題として定式化する。
+\item 上記問題に対し、効率的な準最適解法として**二段階貪欲法**を提案し、その有効性を評価する。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orga9ea643}]{問題定義：通信需要を考慮したリンク忠実度計測問題}
+\begin{itemize}
+\item \alert{\alert{入力}}
+\begin{itemize}
+\item ノードペア集合 \((S, D_n)\)、各ペアの並列リンク集合 \(L_n\)
+\item 各ノードペアの**重要度** \(I_n\)
+\item \alert{\alert{総測定予算}} \(C\)
+\end{itemize}
+\item \alert{\alert{目的}}: ネットワーク全体の**総価値**を最大化する。
+\begin{itemize}
+\item 目的関数: \(\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}\)
+(\$S\textsubscript{sel}\$は選択されたノードペア集合、\$\hat{F}\textsuperscript{*}\textsubscript{n\textsubscript{k}}\$は最高と推定された忠実度)
+\end{itemize}
+\item \alert{\alert{制約条件}}
+\begin{itemize}
+\item 総測定コストが総測定予算 \(C\) を超えないこと。
+\item \(\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C\)
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orge58cc75}]{提案手法：二段階貪欲法 (Two-Phase Greedy)}
+\begin{itemize}
+\item 広域的な探索と集中的な活用を組み合わせ、限られた測定資源を効率的に配分する。
+\item \alert{\alert{第一段階：広域探索フェーズ}}
+\begin{itemize}
+\item 測定予算の一部を全リンクに少量ずつ均等に配分。
+\item 全リンクの忠実度の**初期推定値**を低コストで得る。
+\end{itemize}
+\item \alert{\alert{第二段階：活用フェーズ}}
+\begin{itemize}
+\item \alert{\alert{価値スコア}} (\(= \text{重要度} \times \text{初期推定忠実度}\)) を算出。
+\item スコアが高い有望なノードペア内のリンク群に、残りの測定資源を集中的に投下 (LinkSelFiEを適用)。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org6c8b931}]{実験の目的}
+\begin{itemize}
+\item 提案手法が、限られた測定予算のもとで**ネットワーク全体の総価値**を効率的に最大化できることをシミュレーションにより定量的に示す。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org5ee7765}]{実験シナリオ}
+\begin{itemize}
+\item \alert{\alert{シミュレータ}}: NetSquid
+\item \alert{\alert{トポロジ}}: スター型 (\(N=3\) および \(N=5\))
+\begin{itemize}
+\item 各ノードペア間に5本の並列リンクが存在。
+\end{itemize}
+\item \alert{\alert{忠実度設定}}: 平均0.95のリンク1本、平均0.85のリンク4本（正規分布）
+\item \alert{\alert{重要度}} \(I_n\): 区間 \([0, 1]\) の一様乱数
+\item \alert{\alert{評価指標}}: ネットワーク総価値スコア
+\item \alert{\alert{試行回数}}: 各設定で20回実施し、平均値と95\%信頼区間を算出。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orgae9b2ca}]{比較手法}
+\begin{itemize}
+\item \alert{\alert{提案手法 (Two-Phase Greedy)}}
+\begin{itemize}
+\item 価値スコアに基づき、有望なノードペアに資源を集中配分する。
+\end{itemize}
+\item \alert{\alert{Uniform-LinkSelFiE}}
+\begin{itemize}
+\item 全てのノードペアに測定予算を**均等配分**し、各ペア内でLinkSelFiEを適用する。
+\end{itemize}
+\item \alert{\alert{Uniform-Naive}}
+\begin{itemize}
+\item 全てのリンクに測定予算を**均等配分**する。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org2d57e01}]{測定予算と総価値スコアの関係}
+\begin{itemize}
+\item \begin{center}
+\includegraphics[width=.9\linewidth]{./graphA.eps}
+\end{center} \begin{center}
+\includegraphics[width=.9\linewidth]{./graphC.eps}
+\end{center}
+\item \alert{\alert{考察1}}
+\begin{itemize}
+\item 全ての測定予算条件において、**提案手法が比較手法よりも高い総価値スコアを達成**した。
+\item これは、通信需要と初期推定品質に基づき、価値の高いリンクへ優先的に資源を配分する戦略の有効性を示している。
+\end{itemize}
+\item \alert{\alert{考察2}}
+\begin{itemize}
+\item ノード数が増加すると（\(N=3 \to 5\)）、**提案手法と比較手法との性能差がより拡大**した。
+\item 探索対象が増え資源制約が厳しくなる大規模な状況ほど、提案手法の優位性が際立つことを示唆している。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org1aa5284}]{まとめと今後の課題}
+\#+begin\textsubscript{columns}
+\#+begin\textsubscript{column}: .5\textwidth
+\begin{block}{まとめ}
+\begin{itemize}
+\item 通信需要を考慮したリンク忠実度計測問題を定義し、その準最適解法として**二段階貪欲法**を提案した。
+\item シミュレーション評価により、提案手法が比較手法よりも効率的にネットワーク全体の総価値を高めること、特に**大規模で資源制約が厳しいネットワークにおいて有効**であることを示した。
+\end{itemize}
+\#+end\textsubscript{column}
+\#+begin\textsubscript{column}: .5\textwidth
+\end{block}
+\begin{block}{今後の課題}
+\begin{itemize}
+\item 実際の量子ネットワークで用いられる、より**複雑なトポロジ**における有効性の検証。
+\item 通信需要が時間的に変動する**動的な環境**へのアルゴリズムの適応。
+\item 測定コストだけでなく、他のリソース（エンタングルメント生成時間など）も考慮した多目的最適化。
+\end{itemize}
+\#+end\textsubscript{column}
+\#+end\textsubscript{columns}
+\end{block}
+\end{frame}
+\end{document}

slide.tex~

@@ -0,0 +1,154 @@
+% Created 2025-07-20 Sun 19:43
+\documentclass[compress,dvipdfm,12pt]{beamer}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{amsmath}
+\usepackage[normalem]{ulem}
+\usepackage{hyperref}
+\usetheme{default}
+\begin{document}
+
+
+\begin{frame}[label={sec:org9f48eef}]{背景}
+\begin{itemize}
+\item 量子ネットワークでは、環境ノイズの影響を受けやすいため、高信頼な通信には**忠実度の高い量子リンク**の選択が不可欠。
+\item しかし、リンクの忠実度を正確に推定するには**多大な測定コスト**（時間や量子ビット）を要する。
+\item 限られた測定資源をいかに効率的に配分するかが重要な課題となっている。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org64dd2fd}]{動機}
+\begin{itemize}
+\item 既存のリンク忠実度特定手法（LinkSelFiEなど）は、**各通信経路の重要度（通信需要）を考慮していない**。
+\item すべてのリンク候補を同等に扱うため、通信需要に応じて測定資源を最適に配分できない。
+\item 重要な通信経路の品質を優先的に保証する方が、ネットワーク全体としての価値は高まるはず。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org1a9f864}]{目的}
+\begin{itemize}
+\item 通信需要を**定量的な重み**として導入し、限られた測定資源をリンクの価値に応じて最適に配分する新たな手法を提案する。
+\begin{itemize}
+\item 各通信経路の重要度と忠実度の積をその経路の**価値**と定義。
+\item ネットワーク全体の**総価値を最大化**する問題として定式化する。
+\item 上記問題に対し、効率的な準最適解法として**二段階貪欲法**を提案し、その有効性を評価する。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org79d58bd}]{問題定義：通信需要を考慮したリンク忠実度計測問題}
+\begin{itemize}
+\item \alert{\alert{入力}}
+\begin{itemize}
+\item ノードペア集合 \((S, D_n)\)、各ペアの並列リンク集合 \(L_n\)
+\item 各ノードペアの**重要度** \(I_n\)
+\item \alert{\alert{総測定予算}} \(C\)
+\end{itemize}
+\item \alert{\alert{目的}}: ネットワーク全体の**総価値**を最大化する。
+\begin{itemize}
+\item 目的関数: \(\text{maximize} \sum_{n_k \in S_{sel}} I_{n_k}\hat{F}^*_{n_k}\)
+(\$S\_\{sel\}\$は選択されたノードペア集合、\$\hat{F}\^{}*\_\{n\_k\}\$は最高と推定された忠実度)
+\end{itemize}
+\item \alert{\alert{制約条件}}
+\begin{itemize}
+\item 総測定コストが総測定予算 \(C\) を超えないこと。
+\item \(\sum^N_{n=1} \sum_{l \in L_n} Cost(l) \leq C\)
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orgf0697b8}]{提案手法：二段階貪欲法 (Two-Phase Greedy)}
+\begin{itemize}
+\item 広域的な探索と集中的な活用を組み合わせ、限られた測定資源を効率的に配分する。
+\item \alert{\alert{第一段階：広域探索フェーズ}}
+\begin{itemize}
+\item 測定予算の一部を全リンクに少量ずつ均等に配分。
+\item 全リンクの忠実度の**初期推定値**を低コストで得る。
+\end{itemize}
+\item \alert{\alert{第二段階：活用フェーズ}}
+\begin{itemize}
+\item \alert{\alert{価値スコア}} (\(= \text{重要度} \times \text{初期推定忠実度}\)) を算出。
+\item スコアが高い有望なノードペア内のリンク群に、残りの測定資源を集中的に投下 (LinkSelFiEを適用)。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org6ec3247}]{実験の目的}
+\begin{itemize}
+\item 提案手法が、限られた測定予算のもとで**ネットワーク全体の総価値**を効率的に最大化できることをシミュレーションにより定量的に示す。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org4cdc2f3}]{実験シナリオ}
+\begin{itemize}
+\item \alert{\alert{シミュレータ}}: NetSquid
+\item \alert{\alert{トポロジ}}: スター型 (\(N=3\) および \(N=5\))
+\begin{itemize}
+\item 各ノードペア間に5本の並列リンクが存在。
+\end{itemize}
+\item \alert{\alert{忠実度設定}}: 平均0.95のリンク1本、平均0.85のリンク4本（正規分布）
+\item \alert{\alert{重要度}} \(I_n\): 区間 \([0, 1]\) の一様乱数
+\item \alert{\alert{評価指標}}: ネットワーク総価値スコア
+\item \alert{\alert{試行回数}}: 各設定で20回実施し、平均値と95\%信頼区間を算出。
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:org10edb8a}]{比較手法}
+\begin{itemize}
+\item \alert{\alert{提案手法 (Two-Phase Greedy)}}
+\begin{itemize}
+\item 価値スコアに基づき、有望なノードペアに資源を集中配分する。
+\end{itemize}
+\item \alert{\alert{Uniform-LinkSelFiE}}
+\begin{itemize}
+\item 全てのノードペアに測定予算を**均等配分**し、各ペア内でLinkSelFiEを適用する。
+\end{itemize}
+\item \alert{\alert{Uniform-Naive}}
+\begin{itemize}
+\item 全てのリンクに測定予算を**均等配分**する。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orga261cdf}]{測定予算と総価値スコアの関係}
+\begin{itemize}
+\item \begin{center}
+\includegraphics[width=.9\linewidth]{./graphA.eps}
+\end{center} \begin{center}
+\includegraphics[width=.9\linewidth]{./graphC.eps}
+\end{center}
+\item \alert{\alert{考察1}}
+\begin{itemize}
+\item 全ての測定予算条件において、**提案手法が比較手法よりも高い総価値スコアを達成**した。
+\item これは、通信需要と初期推定品質に基づき、価値の高いリンクへ優先的に資源を配分する戦略の有効性を示している。
+\end{itemize}
+\item \alert{\alert{考察2}}
+\begin{itemize}
+\item ノード数が増加すると（\(N=3 \to 5\)）、**提案手法と比較手法との性能差がより拡大**した。
+\item 探索対象が増え資源制約が厳しくなる大規模な状況ほど、提案手法の優位性が際立つことを示唆している。
+\end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orgf4ad33e}]{まとめと今後の課題}
+\#+begin\_columns
+\#+begin\_column: .5\textwidth
+\begin{block}{まとめ}
+\begin{itemize}
+\item 通信需要を考慮したリンク忠実度計測問題を定義し、その準最適解法として**二段階貪欲法**を提案した。
+\item シミュレーション評価により、提案手法が比較手法よりも効率的にネットワーク全体の総価値を高めること、特に**大規模で資源制約が厳しいネットワークにおいて有効**であることを示した。
+\end{itemize}
+\#+end\_column
+\#+begin\_column: .5\textwidth
+\end{block}
+\begin{block}{今後の課題}
+\begin{itemize}
+\item 実際の量子ネットワークで用いられる、より**複雑なトポロジ**における有効性の検証。
+\item 通信需要が時間的に変動する**動的な環境**へのアルゴリズムの適応。
+\item 測定コストだけでなく、他のリソース（エンタングルメント生成時間など）も考慮した多目的最適化。
+\end{itemize}
+\#+end\_column
+\#+end\_columns
+\end{block}
+\end{frame}
+\end{document}

slideold.org

@@ -0,0 +1,72 @@
+# -*- Org -*-
+# 
+# 
+# Copyright (c) 2010, Hiroyuki Ohsaki.
+# All rights reserved.
+# 
+# $Id: 120111-impact.org,v 1.1 2012/01/12 02:56:04 oosaki Exp oosaki $
+# 
+
+#+STARTUP: beamer
+#+LATEX_CLASS: beamer
+#+LATEX_CLASS_OPTIONS: [compress,dvipdfm,12pt]
+#+OPTIONS:   toc:nil
+#+BEAMER_FRAME_LEVEL: 2
+#+BEAMER_HEADER_EXTRA: \usetheme{Ohsaki}
+#+BEAMER_HEADER_EXTRA: \usepackage{palatino}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\sfdefault}{ppl}
+#+BEAMER_HEADER_EXTRA: \title[On the Impact of Router Virtualization]{On the Impact of Router Virtualization in Content-Centric Networking}
+#+BEAMER_HEADER_EXTRA: \author[K. Tsukamoto]{Keiichiro Tsukamoto\inst{1} and Hiroyuki Ohsaki\inst{1}}
+#+BEAMER_HEADER_EXTRA: \institute{\inst{1} Osaka University, Japan}
+#+BEAMER_HEADER_EXTRA: \date{January 11, 2012}
+#+BEAMER_HEADER_EXTRA: \setlength{\parskip}{1.5ex}
+#+BEAMER_HEADER_EXTRA: \renewcommand{\textbf}{\alert}
+
+
+* 背景
+- aaa
+- aaa
+- aaa  
+
+* 動機
+- aaa
+- aaa
+* 目的
+- aaa
+  - aaa
+  - aaa
+* xxxについて
+- 図
+  - aaa
+  - aaa
+
+* xxxについて
+- aaa
+- aaa
+- aaa
+- aaa
+
+* 実験の目的
+- aaa
+
+* 実験シナリオ
+
+* xxx(用語説明?)
+- aaa
+- aaa
+- aaa
+
+
+* xxxにおけるxxxの影響
+- 図2まい
+  - 考察
+  - 考察
+
+* まとめと今後の課題
+** まとめ
+- aaa
+- aaa
+** 今後の課題
+- aaa
+
+

society25-shun-quantum-slide

@@ -0,0 +1 @@
+Subproject commit 3c17512321644b41249684b7272fc4df4930b63b

test.org

@@ -0,0 +1,12 @@
+#+TITLE: Test Presentation
+#+AUTHOR: A. User
+#+LATEX_CLASS: beamer
+#+LATEX_CLASS_OPTIONS: [dvipdfm]
+#+BEAMER_HEADER_EXTRA: \usetheme{Madrid}
+
+* My First Slide
+This is a test.
+
+* My Second Slide
+Here is some math: $E = mc^2$.
+And here is a formula with a hat: $\hat{H}\psi = E\psi$.

test.tex

@@ -0,0 +1,42 @@
+% Created 2025-07-20 Sun 21:24
+% Intended LaTeX compiler: pdflatex
+\documentclass[dvipdfm]{beamer}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usetheme{default}
+\author{A. User}
+\date{\today}
+\title{Test Presentation}
+\hypersetup{
+ pdfauthor={A. User},
+ pdftitle={Test Presentation},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 28.2 (Org mode 9.5.5)}, 
+ pdflang={English}}
+\begin{document}
+
+\maketitle
+\begin{frame}{Outline}
+\tableofcontents
+\end{frame}
+
+
+\begin{frame}[label={sec:orga995efe}]{My First Slide}
+This is a test.
+\end{frame}
+
+\begin{frame}[label={sec:orgf73ab8b}]{My Second Slide}
+Here is some math: \(E = mc^2\).
+And here is a formula with a hat: \(\hat{H}\psi = E\psi\).
+\end{frame}
+\end{document}

test.tex~

@@ -0,0 +1,25 @@
+% Created 2025-07-20 Sun 20:49
+\documentclass[dvipdfm]{beamer}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{amsmath}
+\usepackage[normalem]{ulem}
+\usepackage{hyperref}
+\usetheme{default}
+\begin{document}
+
+\maketitle
+\begin{frame}{Outline}
+\tableofcontents
+\end{frame}
+
+
+\begin{frame}[label={sec:orgf74b4ca}]{My First Slide}
+This is a test.
+\end{frame}
+
+\begin{frame}[label={sec:org6ec361d}]{My Second Slide}
+Here is some math: \(E = mc^2\).
+And here is a formula with a hat: \(\hat{H}\psi = E\psi\).
+\end{frame}
+\end{document}