Sharp continuity of quantum conditional entropy

2026/07/27 by Mario Berta, Pablo Costa Rico, Gereon Kossmann +2
#quant-ph #math-ph #math.MP

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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 h₂(δ)+δlog(d²-1) up to δ=1-d^-2 and 2log d thereafter, where h₂ denotes the binary entropy. When dim B≥ d, this bound is tight for every δ∈[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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