common-lite.tex

\usepackage{ccicons}
\usepackage{cite}
\usepackage{caption}
\usepackage{xfrac}
\usepackage{xparse}
\usepackage{relsize}
\usepackage{colortbl}
\usepackage{bussproofs}
\usepackage{xcolor}
\usepackage{graphicx}
\usepackage{makeidx}
\usepackage{xstring}
\usepackage{braket}
\usepackage{mathtools}
\usepackage{multicol}
\usepackage{marginnote}
\usepackage{ifthen}
\usepackage{xifthen}
\usepackage{paralist}
\usepackage{calc}
\usepackage{tikz}
\usepackage{tikz-cd}
\usetikzlibrary{calc,arrows,matrix,decorations.pathreplacing}
\usepackage{picins}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{nicefrac}
\usepackage{stmaryrd}
\usepackage{sectsty}
\usepackage{xr}
\usepackage{tikz}
\usepackage[all]{xypic}
\usepackage{hyperref} % <- should be last because it redefined \ref, etc..

\NewDocumentEnvironment{solution}{g}{%
    \leavevmode\unskip%
    \par\vskip.6em\noindent%
    \textPointHeaderI{Solution to~\sref{#1}.}
    }{\leavevmode\unskip\ignorespaces}

\NewDocumentEnvironment{erratum}{g}{%
    \leavevmode\unskip%
    \par\vskip.6em\noindent%
    \textPointHeaderI{Erratum to~\sref{#1}.}
    }{\leavevmode\unskip\ignorespaces}

\NewDocumentEnvironment{addendum}{g}{%
    \leavevmode\unskip%
    \par\vskip.6em\noindent%
    \textPointHeaderI{Addendum to~\sref{#1}.}
    }{\leavevmode\unskip\ignorespaces}

\definecolor{pitchblack}{cmyk}{1 1 1 1}
\definecolor{pitchgray}{cmyk}{.5 .5 .5 .5}

% macros concerning textstyle
\colorlet{darkgreen}{green!50!pitchblack}
\colorlet{darkblue}{blue!75!pitchblack}
\colorlet{lightblue}{blue!50!white}
\colorlet{lightgray}{pitchgray!50!white}
\colorlet{darkgray}{pitchgray!75!pitchblack}
\colorlet{darkred}{red!75!pitchblack}

\allsectionsfont{\sffamily\color{darkblue}}

\newcommand{\textPointHeaderI}[1]{\textcolor{darkblue}{\textbf{\textsf{#1}}}}
\newcommand{\textPointHeaderII}[1]{\textcolor{darkblue}{\textsf{#1}}}
\newcommand{\textPointHeaderIII}[1]{\textcolor{lightgray}{\textsf{#1}}}
\newcommand{\textParsecNumber}[1]{\textcolor{darkblue}{\textbf{\textsf{#1}}}}
\newcommand{\textPointNumberI}[1]{\textcolor{darkblue}{\textsf{#1}}}
\newcommand{\textPointNumberII}[1]{\textcolor{lightblue}{\textsf{#1}}}
\newcommand{\textPointNumberIII}[1]{\textcolor{lightgray}{\textsf{#1}}}
\newcommand{\textDefine}[1]{\textcolor{darkblue}{#1}}
\newcommand{\textSref}[1]{\textsf{#1}}
\newcommand{\textTodo}[1]{\textcolor{darkred}{#1}}
\newcommand{\textRemark}[1]{\textcolor{purple}{#1}}

\newcommand{\Define}[1]{\textDefine{#1}}

\newcommand{\grayed}[1]{\textcolor{darkgray}{#1}}

\renewcommand{\leq}{\leqslant}
\renewcommand{\geq}{\geqslant}
\renewcommand{\nleq}{\not\leqslant}
\renewcommand{\ngeq}{\not\geqslant}

\newcommand{\Cat}[1]{\mathbf{#1}}
\newcommand{\cW}[1]{\Cat{cW}^*_{\text{\textsc{#1}}}}
\newcommand{\haW}[1]{\Cat{haW}^*_{\text{\textsc{#1}}}}
\newcommand{\W}[1]{\Cat{W}^*_{\text{\textsc{#1}}}}
\newcommand{\dW}[1]{\Cat{dW}^*_{\text{\textsc{#1}}}}
\newcommand{\cCstar}[1]{\Cat{cC}^*_{\text{\textsc{#1}}}}
\newcommand{\Cstar}[1]{\Cat{C}^*_{\text{\textsc{#1}}}}
\newcommand{\CH}{\Cat{CH}}
\newcommand{\op}[1]{{#1}{^{\mathsf{op}}}}

\newcommand{\ketbra}[2]{\left|#1\right>\!\left<#2\right|}
\newcommand{\uleq}{\mathbin{\rotatebox[origin=c]{90}{$\leq$}}}
\newcommand{\TR}{\mathop{\mathrm{tr}}}
\newcommand{\wn}{\mathop{\mathrm{wn}}}

\newcommand{\bsp}{\scrB}

\NewDocumentCommand{\vmleq}{o}{\mathrel{%
\IfNoValueTF{#1}{\lesssim}{\lesssim_{#1}}}}

% Common symbols
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\I}{\mathbb{I}}
\newcommand{\spec}{\mathrm{sp}}
\newcommand{\scrA}{\mathscr{A}}
\newcommand{\scrB}{\mathscr{B}}
\newcommand{\scrC}{\mathscr{C}}
\newcommand{\scrD}{\mathscr{D}}
\newcommand{\scrE}{\mathscr{E}}
\newcommand{\scrG}{\mathscr{G}}
\newcommand{\scrH}{\mathscr{H}}
\newcommand{\scrF}{\mathscr{F}}
\newcommand{\scrP}{\mathscr{P}}
\newcommand{\scrK}{\mathscr{K}}
\newcommand{\scrL}{\mathscr{L}}
\newcommand{\scrR}{\mathscr{R}}
\newcommand{\scrS}{\mathscr{S}}
\newcommand{\scrT}{\mathscr{T}}
\newcommand{\scrX}{\mathscr{X}}
\newcommand{\scrY}{\mathscr{Y}}
\newcommand{\scrZ}{\mathscr{Z}}
\newcommand{\scrV}{\mathscr{V}}
\newcommand{\scrW}{\mathscr{W}}

\newcommand{\ceil}[1]{\left\lceil#1\right\rceil}
\newcommand{\cceil}[1]{\left\lceil\!\!\left\lceil#1\right\rceil\!\!\right\rceil}
\newcommand{\cfloor}[1]{\left\lfloor\!\!\left\lfloor#1\right\rfloor\!\!\right\rfloor}
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
\newcommand{\ceill}[1]{\left\lceil#1\right)}
\newcommand{\ceilr}[1]{\left(#1\right\rceil}
\newcommand{\floorl}[1]{\left\lfloor#1\right)}
\newcommand{\floorr}[1]{\left(#1\right\rfloor}
\newcommand{\absl}[1]{\left|#1\right)}
\newcommand{\absr}[1]{\left(#1\right|}

\newcommand{\linf}{\ell^\infty}
\newcommand{\incfun}{\mathcal{J}}
\newcommand{\limp}{\mathbin{\multimap}}
\newcommand{\Mon}{\mathrm{Mon}}
\newcommand{\CMon}{\mathrm{cMon}}
\newcommand{\nsp}{\mathrm{nsp}}
\newcommand{\qbit}{\mathsf{qubit}}
\newcommand{\bit}{\mathsf{bit}}
\DeclarePairedDelimiter{\sem}{\llbracket}{\rrbracket}

\newcommand{\Real}[1]{#1_{\R}}
\newcommand{\Imag}[1]{#1_{\I}}
\newcommand{\sa}[1]{#1_{\R}}
\newcommand{\pos}[1]{#1_{+}}
\newcommand{\bang}{\mathord{!}}

\newcommand\T{\mathrm{t}} % for transpose

\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\length}{length}
\DeclareMathOperator{\interior}{in}
\DeclareMathOperator{\Stat}{Stat}
\DeclareMathOperator{\Pred}{Pred}
\DeclareMathOperator{\Pure}{Pure}
\DeclareMathOperator{\SPred}{SPred}
\DeclareMathOperator{\IM}{im}
%\newcommand\BOX{{\rlap{\kern-1pt\rotatebox[origin=c]{45}{$\diamond$}}\phantom{\diamond}}}
\newcommand\BOX{%
    % {\tikz[baseline]{\draw (-0.3ex,0) rectangle (0.3ex,0.6ex)}}%
    {\rlap{\kern .5pt\tikz[baseline]{\draw[line width=0.08ex] (0,0) rectangle (0.6ex,0.6ex)}}%
    \phantom{\diamond}}}
\DeclareMathOperator{\IMperp}{im^\perp}
\DeclareMathOperator{\cok}{cok}
\DeclareMathOperator{\Par}{Par}
\DeclareMathOperator{\Tot}{Tot}
\newcommand{\andthen}[2]{#1 \mathbin{\&} #2}
\newcommand\asrt{\mathrm{asrt}}
\newcommand\sef{\mathrm{seff}}
\newcommand\pproj{\mathord{\vartriangleright}}
\newcommand{\cmpr}[2]{\ensuremath{\{#1|{\kern.2ex}#2\}}}
\newcommand{\id}{\mathrm{id}}
\DeclareMathOperator{\NStat}{NStat}
\DeclareMathOperator{\Scal}{Scal}
\DeclareMathOperator{\Cont}{C}
\DeclareMathOperator{\Colim}{Colim}
\DeclareMathOperator{\hZ}{hZ}
\DeclareMathOperator{\Inv}{Inv}
\DeclareMathOperator{\Proj}{Proj}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\Ran}{Ran}
\DeclareMathOperator{\Nsb}{Nsb}
\newenvironment{spmatrix}{%
    \left(\begin{smallmatrix}}{%
    \end{smallmatrix}\right)}

\newcommand\after{\mathop{\circ}}
\newcommand\hafter{\mathop{\hat\circ}}
\newcommand\hotimes{\mathbin{\hat{\otimes}}}
\newcommand\ad{\mathrm{ad}}
\newcommand{\uwlim}{\qopname\relax m{uwlim}}
\newcommand{\unlim}{\qopname\relax m{unlim}}
\newcommand{\uslim}{\qopname\relax m{uslim}}
\newcommand\concat{\mathbin{\raisebox{1ex}{\scalebox{.7}{$\frown$}}}}
\newcommand\ncp{\mathrm{ncp}}
\newcommand\pto{\rightharpoonup}
\newcommand\pfrom{\leftharpoonup}
\newcommand{\pullback}[1][dr]{\save*!/#1-1.2pc/#1:(-1,1)@^{|-}\restore}
\newcommand\vN{\mathsf{vN}}
\newcommand\CvN{\mathsf{CvN}}
\newcommand\OUG{\mathsf{OUG}}
\newcommand\EJA{\mathsf{EJA}}
\newcommand\OUS{\mathsf{OUS}}
\newcommand\SET{\mathsf{Set}}
\newcommand\CRng{\mathsf{CRng}}
\newcommand\Rng{\mathsf{Rng}}
\newcommand\bCH{\mathsf{CH}}
\newcommand\AConvM{\mathsf{AConv}_M}
\newcommand\EMod{\mathsf{EMod}}
\newcommand{\bigovee}{\mathop{\vphantom{\sum}\mathchoice%
        {\vcenter{\hbox{\huge $\ovee$}}}%
        {\vcenter{\hbox{\Large $\ovee$}}}%
        {\ovee}{\ovee}}\displaylimits}
\DeclareMathOperator{\Kl}{\mathcal{K}\!\ell}
\newcommand\rfrac[2]{\reflectbox{\nicefrac{\reflectbox{\ensuremath{#1}}}{\reflectbox{\ensuremath{#2}}}}}

\makeatletter
\newcommand{\bigperp}{%
  \mathop{\mathpalette\bigp@rp\relax}%
  \displaylimits
}

\newcommand{\bigp@rp}[2]{%
  \vcenter{
    \m@th\hbox{\scalebox{\ifx#1\displaystyle2.1\else1.5\fi}{$#1\perp$}}
  }%
}
\makeatother


\makeatletter
\def\ourrawref#1{%
    \expandafter\expandafter\expandafter
    \@car\csname r@#1\endcsname\@nil
}
\makeatother

% number a single equation in an align*
% http://tex.stackexchange.com/questions/42726/
\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}

% typesetting theorems
\newcommand{\qed}{\hfill\textcolor{darkblue}{\ensuremath{\square}}}

% NOTE redefined in common.tex
\NewDocumentCommand{\sref}{m}{\textSref{\ref{#1}}}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

% for in main.bib
\newcommand{\doi}[1]{\href{https://doi.org/#1}{doi:#1}}
\newcommand{\arXiv}[1]{\href{https://arxiv.org/abs/#1}{arXiv:#1}}


\newcommand{\purl}[1]{\href{#1}{#1}}

\newcommand{\spacingfix}[0]{\vspace{-1\baselineskip}\ignorespaces}
% used to correct the spacing issues when a point is ended with 
% an \end{enumerate} or \end{equation}

\newcommand{\IGNORE}[1]{}