Every <random unitary channel> satisfies
$$
T(I)=\sum_kp_kU_kIU_k^\dagger
=\left(\sum_kp_k\right)I=I.
$$
It is therefore a <unital quantum channel>.

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 / ii / Solution

A random unitary channel has $T(\rho)=\sum_jp_jU_j\rho U_j^\dagger$. Its Choi matrix is a convex combination of maximally entangled pure states.


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