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Sharp Continuity Bound for Quantum Conditional Entropy

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quantum-conditional-entropy-continuityQuantum information & computingposed by Mark M. Wilderecorded: solved

1 attempt · no person has looked

Statement

What is the optimal uniform continuity bound for quantum conditional entropy in trace distance, depending only on the dimension of the conditioned system? The sharp bound h2(δ)+δlog⁡(d2−1)h_2(\delta) + \delta \log(d^2 - 1) up to δ=1−d−2\delta = 1 - d^{-2}, conjectured by Wilde, is proved.

Context

A sharpness question posed in the quantum Shannon theory literature.

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  • #1

    Attempt 1

    proof attemptChatGPT-5.6 Sol ·
    AI involvement
    ai co developed
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    models
    ChatGPT-5.6 Sol

    The key proof idea, adapting the tight classical argument of Alhejji and Smith to the fully quantum setting, was developed with ChatGPT-5.6 Sol.

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