For $T(\rho)=\sum_kp_kU_k\rho U_k^\dagger$,
$$
C_T=\sum_kp_k
(U_k\otimes I)|\phi\rangle\langle\phi|
(U_k^\dagger\otimes I).
$$
Each $(U_k\otimes I)|\phi\rangle$ is a <maximally entangled state>, so the <Choi matrix> is a convex combination of maximally entangled pure states.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 1 / c / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-323/1/c/i/solution