Sharp continuity of quantum conditional entropy

• URL: http://arxiv.org/abs/2607.24687v1
• Date: Mon, 27 Jul 2026 17:26:52 GMT
• Title: Sharp continuity of quantum conditional entropy
• Abstract summary: We prove sharp uniform continuity bound for quantum conditional entropy.<n>We build on and adapt the tight classical proof of Alhejji & Smith [IEEE ISIT ( 2020)], which follows a conceptually different approach.
• Score: 14.7061334137938
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove the sharp uniform continuity bound for quantum conditional entropy. If two bipartite states are at trace distance at most $δ$ and $d=\dim A$, the optimal dimension-only modulus of continuity is $h_2(δ)+δ\log(d^2-1)$ up to $δ=1-d^{-2}$ and $2\log d$ thereafter, where $h_2$ denotes the binary entropy. When $\dim B\ge d$, this bound is tight for every $δ\in[0,1]$. The key proof idea was developed with the assistance of ChatGPT 5.6 Sol, building on and adapting the tight classical proof of Alhejji \& Smith [IEEE ISIT (2020)], which follows a conceptually different approach.

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