File:Bloch sphere.png

Bloch Sphere

\begin{tikzpicture}[scale=1,every node/.style={minimum size=1cm}] \def\R{4} % sphere radius \def\angEl{25} % elevation angle \def\angAz{-10} % azimuth angle \def\angPhiOne{-20} % longitude of point P \def\angPhiTwo{-110} % longitude of point Q %% working planes \pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole \LongitudePlane[pzplane]{\angEl}{\angPhiOne} \LongitudePlane[qzplane]{\angEl}{\angPhiTwo} \LatitudePlane[equator]{\angEl}{0} \fill[ball color=black!20] (0,0) circle (\R); % 3D lighting effect \coordinate (O) at (0,0); \coordinate[mark coordinate] (N) at (0,\H); \coordinate[mark coordinate] (S) at (0,-\H); \coordinate[mark coordinate] (ON) at (0,1.4*\H); \coordinate[mark coordinate] (OS) at (0,-1.4*\H); \path[qzplane] (-\R,0) coordinate (MXE); \path[pzplane] (-\R,0) coordinate (MPE); \path[qzplane] (\R,0) coordinate (XE); \path[pzplane] (\R,0) coordinate (PE); \path[qzplane] (-2.4*\R,0) coordinate (OMXE); \path[pzplane] (-1.4*\R,0) coordinate (OMPE); \path[qzplane] (2.4*\R,0) coordinate (OXE); \path[pzplane] (1.4*\R,0) coordinate (OPE); \draw[-,thin,blue!45] (ON) -- (N); \draw[-,thin,red!55] (OXE) -- (XE); \draw[-,thin,yellow] (OPE) -- (PE); \draw[-,thin,dashed,blue!45] (OS) -- (S); \draw[-,thin,dashed,red!55] (OMXE) -- (MXE); \draw[-,thin,dashed,yellow] (OMPE) -- (MPE); \draw[->,ultra thick,blue!45] (O) -- (N); \draw[->,ultra thick,red!55] (O) -- (XE); \draw[->,ultra thick,yellow] (O) -- (PE); \draw[->,thin,dashed,blue!45] (O) -- (S); \draw[->,thin,dashed,red!55] (O) -- (MXE); \draw[->,thin,dashed,yellow] (O) -- (MPE); \node[fill=blue!45] at (ON) {$\mathbf{| 1\rangle}'"`UNIQ-MathJax1-QINU`"'\mathbf{| 0\rangle}'"`UNIQ-MathJax2-QINU`"'{| 0\rangle-i\,| 1\rangle\over\sqrt{2}}'"`UNIQ-MathJax3-QINU`"'{| 0\rangle+i\,| 1\rangle\over\sqrt{2}}'"`UNIQ-MathJax4-QINU`"'{| 0\rangle-\,| 1\rangle\over\sqrt{2}}'"`UNIQ-MathJax5-QINU`"'{| 0\rangle+\,| 1\rangle\over\sqrt{2}}$}; \end{tikzpicture}