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‎doc/pub/week3/ipynb/ipynb-week3-src.tar.gz‎

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‎doc/pub/week3/ipynb/week3.ipynb‎

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‎doc/pub/week3/pdf/week3.pdf‎

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‎doc/src/week3/_minted/2A020B28DDA6D7800ACC282582C9C6FB.highlight.minted‎

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‎doc/src/week3/_minted/3A0EE48CE352B97ECBF5AE3E2581FF0C.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{math}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{outer}\PYG{p}{(}\PYG{n}{v}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{n} \PYG{o}{=} \PYG{n+nb}{len}\PYG{p}{(}\PYG{n}{v}\PYG{p}{)}
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\PYG{k}{return} \PYG{p}{[}\PYG{p}{[}\PYG{n}{v}\PYG{p}{[}\PYG{n}{i}\PYG{p}{]}\PYG{o}{*}\PYG{n}{v}\PYG{p}{[}\PYG{n}{j}\PYG{p}{]}\PYG{o}{.}\PYG{n}{conjugate}\PYG{p}{(}\PYG{p}{)} \PYG{k}{for} \PYG{n}{j} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{n}{n}\PYG{p}{)}\PYG{p}{]} \PYG{k}{for} \PYG{n}{i} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{n}{n}\PYG{p}{)}\PYG{p}{]}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{partial\PYGZus{}trace\PYGZus{}B}\PYG{p}{(}\PYG{n}{rho}\PYG{p}{)}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} 2 qubits, basis: |00\PYGZgt{},|01\PYGZgt{},|10\PYGZgt{},|11\PYGZgt{}}
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\PYG{n}{rhoA} \PYG{o}{=} \PYG{p}{[}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{]}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{]}\PYG{p}{]}
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\PYG{k}{for} \PYG{n}{a} \PYG{o+ow}{in} \PYG{p}{(}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{:}
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\PYG{k}{for} \PYG{n}{c} \PYG{o+ow}{in} \PYG{p}{(}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{s} \PYG{o}{=} \PYG{l+m+mi}{0}\PYG{n}{j}
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\PYG{k}{for} \PYG{n}{b} \PYG{o+ow}{in} \PYG{p}{(}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{i} \PYG{o}{=} \PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{a} \PYG{o}{+} \PYG{n}{b}
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\PYG{n}{j} \PYG{o}{=} \PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{c} \PYG{o}{+} \PYG{n}{b}
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\PYG{n}{s} \PYG{o}{+}\PYG{o}{=} \PYG{n}{rho}\PYG{p}{[}\PYG{n}{i}\PYG{p}{]}\PYG{p}{[}\PYG{n}{j}\PYG{p}{]}
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\PYG{n}{rhoA}\PYG{p}{[}\PYG{n}{a}\PYG{p}{]}\PYG{p}{[}\PYG{n}{c}\PYG{p}{]} \PYG{o}{=} \PYG{n}{s}
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\PYG{k}{return} \PYG{n}{rhoA}
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\PYG{c+c1}{\PYGZsh{} Bell states as length\PYGZhy{}4 vectors}
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\PYG{n}{inv} \PYG{o}{=} \PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{math}\PYG{o}{.}\PYG{n}{sqrt}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{)}
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\PYG{n}{Phi\PYGZus{}plus} \PYG{o}{=} \PYG{p}{[}\PYG{n}{inv}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{n}{inv}\PYG{p}{]}
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\PYG{n}{Phi\PYGZus{}minus} \PYG{o}{=} \PYG{p}{[}\PYG{n}{inv}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{o}{\PYGZhy{}}\PYG{n}{inv}\PYG{p}{]}
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\PYG{n}{Psi\PYGZus{}plus} \PYG{o}{=} \PYG{p}{[}\PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{n}{inv}\PYG{p}{,} \PYG{n}{inv}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{]}
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\PYG{n}{Psi\PYGZus{}minus} \PYG{o}{=} \PYG{p}{[}\PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{n}{inv}\PYG{p}{,} \PYG{o}{\PYGZhy{}}\PYG{n}{inv}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{]}
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\PYG{k}{for} \PYG{n}{name}\PYG{p}{,} \PYG{n}{psi} \PYG{o+ow}{in} \PYG{p}{[}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Phi+}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{Phi\PYGZus{}plus}\PYG{p}{)}\PYG{p}{,} \PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Phi\PYGZhy{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{Phi\PYGZus{}minus}\PYG{p}{)}\PYG{p}{,}
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\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Psi+}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{Psi\PYGZus{}plus}\PYG{p}{)}\PYG{p}{,} \PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Psi\PYGZhy{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{Psi\PYGZus{}minus}\PYG{p}{)}\PYG{p}{]}\PYG{p}{:}
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\PYG{n}{rhoAB} \PYG{o}{=} \PYG{n}{outer}\PYG{p}{(}\PYG{n}{psi}\PYG{p}{)}
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\PYG{n}{rhoA} \PYG{o}{=} \PYG{n}{partial\PYGZus{}trace\PYGZus{}B}\PYG{p}{(}\PYG{n}{rhoAB}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} convert to plain real for the eig solver}
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\PYG{n}{rhoA\PYGZus{}real} \PYG{o}{=} \PYG{p}{[}\PYG{p}{[}\PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{,} \PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{]}\PYG{p}{,}
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\PYG{p}{[}\PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{,} \PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{]}\PYG{p}{]}
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\PYG{n}{lams} \PYG{o}{=} \PYG{n}{eigvals\PYGZus{}2x2}\PYG{p}{(}\PYG{n}{rhoA\PYGZus{}real}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{name}\PYG{p}{,} \PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{rhoA eigenvalues:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{lams}\PYG{p}{,} \PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{S(rhoA)=}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{S\PYGZus{}vn\PYGZus{}from\PYGZus{}eigs}\PYG{p}{(}\PYG{n}{lams}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week3/_minted/405916FECA88CD90BB2F255776B90A99.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{numpy}\PYG{+w}{ }\PYG{k}{as}\PYG{+w}{ }\PYG{n+nn}{np}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{vn\PYGZus{}entropy}\PYG{p}{(}\PYG{n}{rho}\PYG{p}{)}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} eigenvalues of Hermitian matrix}
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\PYG{n}{w} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{linalg}\PYG{o}{.}\PYG{n}{eigvalsh}\PYG{p}{(}\PYG{n}{rho}\PYG{p}{)}
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\PYG{n}{w} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{maximum}\PYG{p}{(}\PYG{n}{w}\PYG{p}{,} \PYG{l+m+mf}{0.0}\PYG{p}{)}
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\PYG{n}{w} \PYG{o}{=} \PYG{n}{w}\PYG{p}{[}\PYG{n}{w} \PYG{o}{\PYGZgt{}} \PYG{l+m+mf}{1e\PYGZhy{}15}\PYG{p}{]}
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\PYG{k}{return} \PYG{o}{\PYGZhy{}}\PYG{n}{np}\PYG{o}{.}\PYG{n}{sum}\PYG{p}{(}\PYG{n}{w}\PYG{o}{*}\PYG{n}{np}\PYG{o}{.}\PYG{n}{log2}\PYG{p}{(}\PYG{n}{w}\PYG{p}{)}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} Bell state |Phi+\PYGZgt{}}
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\PYG{n}{psi} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{array}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{,} \PYG{n}{dtype}\PYG{o}{=}\PYG{n+nb}{complex}\PYG{p}{)}\PYG{o}{/}\PYG{n}{np}\PYG{o}{.}\PYG{n}{sqrt}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{)}
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\PYG{n}{rhoAB} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{outer}\PYG{p}{(}\PYG{n}{psi}\PYG{p}{,} \PYG{n}{psi}\PYG{o}{.}\PYG{n}{conj}\PYG{p}{(}\PYG{p}{)}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} partial trace over B}
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\PYG{n}{rhoA} \PYG{o}{=} \PYG{n}{np}\PYG{o}{.}\PYG{n}{zeros}\PYG{p}{(}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{,}\PYG{l+m+mi}{2}\PYG{p}{)}\PYG{p}{,} \PYG{n}{dtype}\PYG{o}{=}\PYG{n+nb}{complex}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{a} \PYG{o+ow}{in} \PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{:}
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\PYG{k}{for} \PYG{n}{c} \PYG{o+ow}{in} \PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{:}
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\PYG{k}{for} \PYG{n}{b} \PYG{o+ow}{in} \PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{:}
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\PYG{n}{rhoA}\PYG{p}{[}\PYG{n}{a}\PYG{p}{,}\PYG{n}{c}\PYG{p}{]} \PYG{o}{+}\PYG{o}{=} \PYG{n}{rhoAB}\PYG{p}{[}\PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{a}\PYG{o}{+}\PYG{n}{b}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{o}{*}\PYG{n}{c}\PYG{o}{+}\PYG{n}{b}\PYG{p}{]}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{vn\PYGZus{}entropy}\PYG{p}{(}\PYG{n}{rhoA}\PYG{p}{)}\PYG{p}{)} \PYG{c+c1}{\PYGZsh{} should print 1.0}
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\end{MintedVerbatim}

‎doc/src/week3/_minted/4EAE9C00F4D3B0C3BF5EA09CF02D879E.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{math}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{H2}\PYG{p}{(}\PYG{n}{p}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{eps} \PYG{o}{=} \PYG{l+m+mf}{1e\PYGZhy{}15}
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\PYG{n}{p} \PYG{o}{=} \PYG{n+nb}{min}\PYG{p}{(}\PYG{n+nb}{max}\PYG{p}{(}\PYG{n}{p}\PYG{p}{,} \PYG{n}{eps}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mf}{1.0}\PYG{o}{\PYGZhy{}}\PYG{n}{eps}\PYG{p}{)}
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\PYG{k}{return} \PYG{o}{\PYGZhy{}}\PYG{n}{p}\PYG{o}{*}\PYG{n}{math}\PYG{o}{.}\PYG{n}{log}\PYG{p}{(}\PYG{n}{p}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{p}{)} \PYG{o}{\PYGZhy{}} \PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{\PYGZhy{}}\PYG{n}{p}\PYG{p}{)}\PYG{o}{*}\PYG{n}{math}\PYG{o}{.}\PYG{n}{log}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{\PYGZhy{}}\PYG{n}{p}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{p} \PYG{o+ow}{in} \PYG{p}{[}\PYG{l+m+mf}{0.0}\PYG{p}{,} \PYG{l+m+mf}{0.1}\PYG{p}{,} \PYG{l+m+mf}{0.25}\PYG{p}{,} \PYG{l+m+mf}{0.5}\PYG{p}{,} \PYG{l+m+mf}{0.75}\PYG{p}{,} \PYG{l+m+mf}{0.9}\PYG{p}{,} \PYG{l+m+mf}{1.0}\PYG{p}{]}\PYG{p}{:}
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\PYG{c+c1}{\PYGZsh{} clamp for endpoints}
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\PYG{n}{pp} \PYG{o}{=} \PYG{n+nb}{min}\PYG{p}{(}\PYG{n+nb}{max}\PYG{p}{(}\PYG{n}{p}\PYG{p}{,} \PYG{l+m+mf}{1e\PYGZhy{}15}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{1}\PYG{o}{\PYGZhy{}}\PYG{l+m+mf}{1e\PYGZhy{}15}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{n}{p}\PYG{p}{,} \PYG{n}{H2}\PYG{p}{(}\PYG{n}{pp}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week3/_minted/5205F35DBA799D421FE7C32910AE80E9.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{math}\PYG{o}{,}\PYG{+w}{ }\PYG{n+nn}{cmath}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{eigvals\PYGZus{}2x2}\PYG{p}{(}\PYG{n}{rho}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{a}\PYG{p}{,} \PYG{n}{b} \PYG{o}{=} \PYG{n}{rho}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}
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\PYG{n}{c}\PYG{p}{,} \PYG{n}{d} \PYG{o}{=} \PYG{n}{rho}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}
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\PYG{n}{tr} \PYG{o}{=} \PYG{n}{a} \PYG{o}{+} \PYG{n}{d}
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\PYG{n}{det} \PYG{o}{=} \PYG{n}{a}\PYG{o}{*}\PYG{n}{d} \PYG{o}{\PYGZhy{}} \PYG{n}{b}\PYG{o}{*}\PYG{n}{c}
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\PYG{n}{disc} \PYG{o}{=} \PYG{n}{tr}\PYG{o}{*}\PYG{n}{tr} \PYG{o}{\PYGZhy{}} \PYG{l+m+mi}{4}\PYG{o}{*}\PYG{n}{det}
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\PYG{n}{root} \PYG{o}{=} \PYG{n}{cmath}\PYG{o}{.}\PYG{n}{sqrt}\PYG{p}{(}\PYG{n}{disc}\PYG{p}{)}
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\PYG{n}{lam1} \PYG{o}{=} \PYG{l+m+mf}{0.5}\PYG{o}{*}\PYG{p}{(}\PYG{n}{tr} \PYG{o}{+} \PYG{n}{root}\PYG{p}{)}
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\PYG{n}{lam2} \PYG{o}{=} \PYG{l+m+mf}{0.5}\PYG{o}{*}\PYG{p}{(}\PYG{n}{tr} \PYG{o}{\PYGZhy{}} \PYG{n}{root}\PYG{p}{)}
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\PYG{c+c1}{\PYGZsh{} return real parts (should be real for Hermitian rho)}
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\PYG{k}{return} \PYG{p}{[}\PYG{n}{lam1}\PYG{o}{.}\PYG{n}{real}\PYG{p}{,} \PYG{n}{lam2}\PYG{o}{.}\PYG{n}{real}\PYG{p}{]}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{S\PYGZus{}vn\PYGZus{}from\PYGZus{}eigs}\PYG{p}{(}\PYG{n}{lams}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{S} \PYG{o}{=} \PYG{l+m+mf}{0.0}
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\PYG{k}{for} \PYG{n}{lam} \PYG{o+ow}{in} \PYG{n}{lams}\PYG{p}{:}
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\PYG{n}{lam} \PYG{o}{=} \PYG{n+nb}{max}\PYG{p}{(}\PYG{n}{lam}\PYG{p}{,} \PYG{l+m+mf}{0.0}\PYG{p}{)}
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\PYG{k}{if} \PYG{n}{lam} \PYG{o}{\PYGZgt{}} \PYG{l+m+mf}{1e\PYGZhy{}15}\PYG{p}{:}
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\PYG{n}{S} \PYG{o}{\PYGZhy{}}\PYG{o}{=} \PYG{n}{lam}\PYG{o}{*}\PYG{n}{math}\PYG{o}{.}\PYG{n}{log}\PYG{p}{(}\PYG{n}{lam}\PYG{p}{,} \PYG{l+m+mi}{2}\PYG{p}{)}
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\PYG{k}{return} \PYG{n}{S}
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\PYG{n}{rhoA} \PYG{o}{=} \PYG{p}{[}\PYG{p}{[}\PYG{l+m+mf}{0.5}\PYG{p}{,} \PYG{l+m+mf}{0.0}\PYG{p}{]}\PYG{p}{,}
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\PYG{p}{[}\PYG{l+m+mf}{0.0}\PYG{p}{,} \PYG{l+m+mf}{0.5}\PYG{p}{]}\PYG{p}{]}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{eigvals:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{eigvals\PYGZus{}2x2}\PYG{p}{(}\PYG{n}{rhoA}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{S(rhoA):}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{S\PYGZus{}vn\PYGZus{}from\PYGZus{}eigs}\PYG{p}{(}\PYG{n}{eigvals\PYGZus{}2x2}\PYG{p}{(}\PYG{n}{rhoA}\PYG{p}{)}\PYG{p}{)}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week3/_minted/69EB0BFB7F9F39B351AF8572A172CAFD.highlight.minted‎

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\begin{MintedVerbatim}[commandchars=\\\{\},codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax}]
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\PYG{k+kn}{import}\PYG{+w}{ }\PYG{n+nn}{math}
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\PYG{k}{def}\PYG{+w}{ }\PYG{n+nf}{psi\PYGZus{}theta}\PYG{p}{(}\PYG{n}{theta}\PYG{p}{)}\PYG{p}{:}
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\PYG{k}{return} \PYG{p}{[}\PYG{n}{math}\PYG{o}{.}\PYG{n}{cos}\PYG{p}{(}\PYG{n}{theta}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{l+m+mi}{0}\PYG{n}{j}\PYG{p}{,} \PYG{n}{math}\PYG{o}{.}\PYG{n}{sin}\PYG{p}{(}\PYG{n}{theta}\PYG{p}{)}\PYG{p}{]}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{theta S(rhoA)}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\PYG{k}{for} \PYG{n}{k} \PYG{o+ow}{in} \PYG{n+nb}{range}\PYG{p}{(}\PYG{l+m+mi}{11}\PYG{p}{)}\PYG{p}{:}
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\PYG{n}{theta} \PYG{o}{=} \PYG{p}{(}\PYG{n}{math}\PYG{o}{.}\PYG{n}{pi}\PYG{o}{/}\PYG{l+m+mi}{2}\PYG{p}{)} \PYG{o}{*} \PYG{n}{k}\PYG{o}{/}\PYG{l+m+mi}{10}
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\PYG{n}{psi} \PYG{o}{=} \PYG{n}{psi\PYGZus{}theta}\PYG{p}{(}\PYG{n}{theta}\PYG{p}{)}
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\PYG{n}{rhoAB} \PYG{o}{=} \PYG{n}{outer}\PYG{p}{(}\PYG{n}{psi}\PYG{p}{)}
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\PYG{n}{rhoA} \PYG{o}{=} \PYG{n}{partial\PYGZus{}trace\PYGZus{}B}\PYG{p}{(}\PYG{n}{rhoAB}\PYG{p}{)}
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\PYG{n}{rhoA\PYGZus{}real} \PYG{o}{=} \PYG{p}{[}\PYG{p}{[}\PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{,} \PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{]}\PYG{p}{,}
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\PYG{p}{[}\PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{,} \PYG{n}{rhoA}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{o}{.}\PYG{n}{real}\PYG{p}{]}\PYG{p}{]}
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\PYG{n}{S} \PYG{o}{=} \PYG{n}{S\PYGZus{}vn\PYGZus{}from\PYGZus{}eigs}\PYG{p}{(}\PYG{n}{eigvals\PYGZus{}2x2}\PYG{p}{(}\PYG{n}{rhoA\PYGZus{}real}\PYG{p}{)}\PYG{p}{)}
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\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+sa}{f}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+si}{\PYGZob{}}\PYG{n}{theta}\PYG{l+s+si}{:}\PYG{l+s+s2}{6.3f}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{ }\PYG{l+s+si}{\PYGZob{}}\PYG{n}{S}\PYG{l+s+si}{:}\PYG{l+s+s2}{8.6f}\PYG{l+s+si}{\PYGZcb{}}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
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\end{MintedVerbatim}

‎doc/src/week3/_minted/_3D4C21A9C8D362A9F60459A7BE3AA26E.index.minted‎

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