Figure 12

The unitary evolution path for the mixed state. The state vector of the initial mixed state is prepared to be along -x axis pointing to A. It evolves along the path A–B–C–D–A to return back to point to A. Ω is the solid angle enclosed by this path. \(\theta =\Omega /4\) is the angle between the x–y plane and either of the half paths (A–B–C or C–D–A)