{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24687",
  "author_total": 5,
  "authors": [
    {
      "name": "Mario Berta"
    },
    {
      "name": "Pablo Costa Rico"
    },
    {
      "name": "Gereon Kossmann"
    },
    {
      "name": "Ludovico Lami"
    },
    {
      "name": "Julius A. Zeiss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26t015nzc6a0c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24687",
  "fulltext_url": null,
  "id": "26t015nzc6a0c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24687",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7171561057",
  "pdf_url": "https://arxiv.org/pdf/2607.24687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26t015nzc6a0c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2607.24687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24687"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sharp continuity of quantum conditional entropy",
  "title_text": "Sharp continuity of quantum conditional entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/26t015nzc6a0c",
  "venue": "arXiv",
  "versions": []
}