The <Kraus representation> is
$$
\boxed{T(\rho)=\sum_jK_j\rho K_j^\dagger},
\qquad
\boxed{\sum_jK_j^\dagger K_j=I}.
$$
The second identity is precisely trace preservation. Different Kraus families related by an isometry represent the same 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 / a / ii / Solution

 Solution

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