{"paper":{"title":"Sharp continuity of quantum conditional entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Gereon Kossmann, Julius A. Zeiss, Ludovico Lami, Mario Berta, Pablo Costa Rico","submitted_at":"2026-07-27T17:26:52Z","abstract_excerpt":"We prove the sharp uniform continuity bound for quantum conditional entropy. If two bipartite states are at trace distance at most $\\delta$ and $d=\\dim A$, the optimal dimension-only modulus of continuity is $h_2(\\delta)+\\delta\\log(d^2-1)$ up to $\\delta=1-d^{-2}$ and $2\\log d$ thereafter, where $h_2$ denotes the binary entropy. When $\\dim B\\ge d$, this bound is tight for every $\\delta\\in[0,1]$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24687","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24687/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}