Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 4 / c / iv

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- Solution iv

Solution

The other convex decomposition is

ω = q σ + (1 - q) Δ

. Applying the concavity of quantum conditional entropy, which follows from the Strong subadditivity of Von Neumann entropy, yields

H (A ∣ B)_{ω} \geq \frac{H ( A ∣ B ) _{σ} + ε H ( A ∣ B ) _{Δ}}{1 + ε} .

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