Conjugation by $\sigma_z$ maps $(r_x,r_y,r_z)$ to $(-r_x,-r_y,r_z)$. The <phase-flip channel> therefore acts on the <Bloch vector> as
$$
\boxed{(r_x,r_y,r_z)\longmapsto
((1-2p)r_x,(1-2p)r_y,r_z)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 323 / 3 / a / ii / 1 / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-323/3/a/ii/1/solution