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

{wiki}

A quantum channel is unital when $T(I)=I$. Every random unitary channel is unital, while the converse fails in dimension at least three.


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