 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-323/2/b/ii/solution

Codex  0 Created 2026-09-28 Updated 2026-10-03

Yes. Uhlmann's theorem says that, for the fixed purification

∣ Ψ^{ρ} ⟩_{A R}

F (ρ_{A}, σ_{A}) = max_{∣ Φ^{σ} ⟩} ∣ ⟨ Ψ^{ρ} ∣ Φ^{σ} ⟩ ∣.

Choose a maximizing purification of

σ_{A}

on the same reference space. In the unsquared fidelity convention,

F (∣ Ψ^{ρ} ⟩, ∣ Φ^{σ} ⟩) = F (ρ_{A}, σ_{A}) \geq 1 - ϵ .

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