View source for 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) {$\mathbf{| 1\rangle}$};
\node[fill=blue!45] at (OS) {$\mathbf{| 0\rangle}$};
\node[fill=yellow] at (OMPE) {${| 0\rangle-i\,| 1\rangle\over\sqrt{2}}$};
\node[fill=yellow] at (OPE) {${| 0\rangle+i\,| 1\rangle\over\sqrt{2}}$};
\node[fill=red!55] at (OMXE) {${| 0\rangle-\,| 1\rangle\over\sqrt{2}}$};
\node[fill=red!55] at (OXE) {${| 0\rangle+\,| 1\rangle\over\sqrt{2}}$};
\end{tikzpicture}