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Sharp Continuity Bound for Quantum Conditional Entropy

Quantum information & computing · posed by Mark M. Wilde · solved

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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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    ChatGPT-5.6 Sol

    No person is named on this work: the record names only the tool it came from, and no ProbXiv account is credited for it.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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