\NeedsTeXFormat{LaTeX2e}[1999/12/01]
\ProvidesPackage{quantum}
 [2011/01/23 v0.2.1 Dirac notation, operator commands,
 and other quantum stuff]

% need amsmath for all kinds of stuff
\usepackage{amsmath}
% need blackboard fonts for identity and field symbols
\usepackage{bbm}

%---- identity symbol ----
\newcommand{\identity}{\mathbbm{1}}
%\newcommand{\identity}{\mbox{$1 \hspace{-1.0mm} {\bf l}$}}

% various fields
\newcommand{\RR}{\mathbbm{R}}
\newcommand{\CC}{\mathbbm{C}}
\newcommand{\FF}{\mathbbm{F}}
\newcommand{\NN}{\mathbbm{N}}
\newcommand{\ZZ}{\mathbbm{Z}}
\newcommand{\PP}{\mathbbm{P}}
\newcommand{\QQ}{\mathbbm{Q}}
\newcommand{\UU}{\mathbbm{U}}
\newcommand{\EE}{\mathbbm{E}}



%---- basic Dirac notation ----%
%\newcommand{\bra}[2][]{\mathinner{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle #1}}\hspace{-0.2em}\langle #2|}}
\newcommand{\bra}[2][]{\mathinner{\langle #2|}_{#1}}
\newcommand{\ket}[2][]{\mathinner{|#2\rangle}_{\hspace{-0.1em}#1}}
%\newcommand{\Bra}[2][]{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle{#1}}}\hspace{-0.2em}\left<#2\right|}
\newcommand{\Bra}[2][]{\left<#2\right|_{#1}}
\newcommand{\Ket}[2][]{\left|#2\right>_{\hspace{-0.1em}#1}}
%\newcommand{\bigBra}[2][]{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle{#1}}}\hspace{-0.2em}\bigl<#2\bigr|}
\newcommand{\bigBra}[2][]{\bigl<#2\bigr|_{#1}}
\newcommand{\bigKet}[2][]{\bigl|#2\bigr>_{\hspace{-0.1em}#1}}
%\newcommand{\BigBra}[2][]{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle{#1}}}\hspace{-0.2em}\Bigl<#2\Bigr|}
\newcommand{\BigBra}[2][]{\Bigl<#2\Bigr|_{#1}}
\newcommand{\BigKet}[2][]{\Bigl|#2\Bigr>_{\hspace{-0.1em}#1}}
%\newcommand{\biggBra}[2][]{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle{#1}}}\hspace{-0.2em}\biggl<#2\biggr|}
\newcommand{\biggBra}[2][]{\biggl<#2\biggr|_{#1}}
\newcommand{\biggKet}[2][]{\biggl|#2\biggr>_{\hspace{-0.1em}#1}}
%\newcommand{\BiggBra}[2][]{\raisebox{-0.3em}
%  {\ensuremath{\scriptstyle{#1}}}\hspace{-0.2em}\Biggl<#2\Biggr|}
\newcommand{\BiggBra}[2][]{\Biggl<#2\Biggr|_{#1}}
\newcommand{\BiggKet}[2][]{\Biggl|#2\Biggr>_{\hspace{-0.1em}#1}}

%---- compound Dirac notation ----
\newcommand{\braket}[3][]{\mathinner{\langle #2|#3\rangle}_{\hspace{-0.1em}#1}}
%\newcommand{\ketbra}[3][]{\mathinner{|#2\rangle
%  \raisebox{-0.3em}{\ensuremath{\scriptstyle #1}}\langle #3|}}
\newcommand{\ketbra}[3][]{\mathinner{|#2\rangle\langle #3|}_{#1}}
\newcommand{\Braket}[3][]{\left<#2\middle|#3\right>_{\hspace{-0.1em}#1}}
%\newcommand{\Ketbra}[3][]{\left|#2\vphantom{#3}\right>\hspace{-0.2em}%
%  \raisebox{-0.3em}{\ensuremath{\scriptstyle #1}}\hspace{-0.2em}%
%  \left<#3\vphantom{#2}\right|}
\newcommand{\Ketbra}[3][]{\left|#2\middle>\middle<#3\right|_{#1}}
\newcommand{\braKet}[3]{\mathinner{\langle #1|#2|#3 \rangle}}
\newcommand{\BraKet}[3]{\left< #1\vphantom{#2}\right|
  #2\left|#3 \vphantom{#2}\right>}
\newcommand{\proj}[2][]{\ketbra[#1]{#2}{#2}}
\newcommand{\Proj}[2][]{\Ketbra[#1]{#2}{#2}}

%---- expectation values ----
\newcommand{\expect}[1]{\mathinner{\langle #1\rangle}}
\newcommand{\Expect}[1]{\left< #1 \right>}
\newcommand{\bigExpect}[1]{\bigl< #1 \bigr>}
\newcommand{\BigExpect}[1]{\Bigl< #1 \Bigr>}
\newcommand{\biggExpect}[1]{\biggl< #1 \biggr>}
\newcommand{\BiggExpect}[1]{\Biggl< #1 \Biggr>}

%---- miscelaneous quantum notation ----
\newcommand{\prj}{\Pi}
\newcommand{\comm}[2]{[#1,#2]}
\newcommand{\Comm}[2]{\left[#1,#2\right]}
\newcommand{\Anticomm}[2]{\left\{#1,#2\right\}}
\newcommand{\anticomm}[2]{\{#1,#2\}}

%---- norms ----
\newcommand{\abs}[1]{|#1|}
\newcommand{\Abs}[1]{\left\vert #1\right\vert}
\newcommand{\bigAbs}[1]{\bigl\vert #1\bigr\vert}
\newcommand{\BigAbs}[1]{\Bigl\vert #1\Bigr\vert}
\newcommand{\biggAbs}[1]{\biggl\vert #1\biggr\vert}
\newcommand{\BiggAbs}[1]{\Biggl\vert #1\Biggr\vert}
\newcommand{\matnorm}[1]{\|#1\|}
\newcommand{\Matnorm}[1]{\left\lVert #1\right\rVert}
\newcommand{\bigMatnorm}[1]{\bigl\lVert #1\bigr\rVert}
\newcommand{\BigMatnorm}[1]{\Bigl\lVert #1\Bigr\rVert}
\newcommand{\biggMatnorm}[1]{\biggl\lVert #1\biggr\rVert}
\newcommand{\BiggMatnorm}[1]{\Biggl\lVert #1\Biggr\rVert}
\newcommand{\MatnormHS}[1]{\Matnorm{#1}_{\mathrm{HS}}}
\newcommand{\matnormHS}[1]{\matnorm{#1}_{\mathrm{HS}}}
\newcommand{\MatnormTr}[1]{\Matnorm{#1}_{\mathrm{tr}}}
\newcommand{\matnormTr}[1]{\matnorm{#1}_{\mathrm{tr}}}
\newcommand{\MatnormF}[1]{\Matnorm{#1}_{\mathrm{F}}}
\newcommand{\matnormF}[1]{\matnorm{#1}_{\mathrm{F}}}


%---- Horizontal version of \smash ----
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}}
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathllap{\mathpalette\mathllapinternal}
\def\mathrlap{\mathpalette\mathrlapinternal}
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}
\def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}}


%---- Shorthands ----
\DeclareMathOperator{\tr}{Tr}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\real}{Re}
\DeclareMathOperator{\imag}{Im}
\DeclareMathOperator{\pfaf}{Pf}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\vspan}{span}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\schmidt}{Sch}
\DeclareMathOperator{\prob}{Pr}
\newcommand{\ox}{\otimes}
\newcommand{\dg}{\dagger}
\newcommand{\Span}[1]{\vspan\left\{#1\right\}}
%\newcommand{\1}{\identity}
\newcommand{\id}{\identity}
\newcommand{\expectation}{\mathbb{E}}
\newcommand{\order}[1]{O({#1})}
\newcommand{\Order}[1]{O\left({#1}\right)}
\newcommand{\bigOrder}[1]{O\bigl({#1}\bigr)}
\newcommand{\BigOrder}[1]{O\Bigl({#1}\Bigr)}
\newcommand{\biggOrder}[1]{O\biggl({#1}\biggr)}
\newcommand{\BiggOrder}[1]{O\Biggl({#1}\Biggr)}
\newcommand{\bipartition}[2]{#1|#2}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\dt}{\delta t}
\newcommand{\HS}{\mathcal{H}}
\newcommand{\ebit}{\mathrm{ebit}}
\newcommand{\hc}{\mathrm{h.c.}}
\newcommand{\Wlog}{w.l.o.g.}
\newcommand{\WLOG}{W.l.o.g.}
\newcommand{\etal}{\textit{et al.}}


\endinput
%%
%% End of file `quantum.sty'