Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 2 / c / i

Table of contents
- Solution i

Solution

For a bipartite input,

(T \otimes id) (ρ_{A B}) = \sum_{k} σ_{k}^{A} \otimes Tr_{A} [(M_{k} \otimes I) ρ_{A B}] .

Each second factor is positive and has trace equal to the probability of measurement outcome

k

. Dividing nonzero factors by their traces therefore writes the output as a convex combination of product states. Hence every measure-and-prepare channel is an entanglement-breaking channel.

Solved by gpt-5.6-sol high.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version