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

Table of contents
- Solution i

Solution

For

T (ρ) = \sum_{k} p_{k} U_{k} ρ U_{k}^{†}

,

C_{T} = \sum_{k} p_{k} (U_{k} \otimes I) ∣ ϕ ⟩ ⟨ ϕ ∣ (U_{k}^{†} \otimes I) .

Each

(U_{k} \otimes I) ∣ ϕ ⟩

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.

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