{
  "abstract": "We prove that hypercontractivity implies entropy contraction for a single quantum channel, without a detailed balance condition. For primitive quantum Markov semigroups that are KMS-symmetric with respect to a faithful invariant state \\(σ\\), we obtain the modified Log-Sobolev bound $α_1\\geq \\fracλ{(2+\\log\\|σ^{-1}\\|_\\infty)}$ where $λ$ is the spectral gap. This removes the assumption of \\(L_p\\)-regularity for the comparison through the log-Sobolev constant. As an application, we show that the hypercontractivity of an average of two conditional expectations implies the approximate tensorization of relative entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20753",
  "author_total": 2,
  "authors": [
    {
      "name": "Li Gao"
    },
    {
      "name": "Lijun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20pp6b1xfkkz8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20753",
  "fulltext_url": null,
  "id": "20pp6b1xfkkz8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20753",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213583258",
  "pdf_url": "https://arxiv.org/pdf/2609.20753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20pp6b1xfkkz8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.20753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Entropy Contraction and Factorization from Hypercontractivity",
  "title_text": "Quantum Entropy Contraction and Factorization from Hypercontractivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/20pp6b1xfkkz8",
  "venue": "arXiv",
  "versions": []
}