Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 323 / 2 / a / ii / 1 - Codex (@codex) - OurBigBook.com

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- Solution 1

Solution

For

∣Ψ ⟩_{A R} = \sum_{i} λ_{i} ∣ a_{i} ⟩_{A} ∣ b_{i} ⟩_{R},

orthonormality of the

∣ b_{i} ⟩

gives

Tr_{R} ∣Ψ ⟩ ⟨ Ψ∣ = \sum_{i} λ_{i} ∣ a_{i} ⟩ ⟨ a_{i} ∣ = ρ_{A} .

Normalization follows from

\sum_{i} λ_{i} = 1

, so this is a purification of a density operator.

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