{
  "abstract": "In this paper, we construct primitive KMS-symmetric quantum Markov semigroups for which the $p$-logarithmic Sobolev constant vanishes at $p=1/2$ and a correlated graph-based example for which the $p$-logarithmic Sobolev constant tends to $-\\infty$ as $p\\to 0^+$. These examples obstruct a positive uniform reverse-hypercontractivity rate on $(0,1)$. By contrast, we show that every primitive KMS-symmetric quantum Markov semigroup satisfies quantum reverse hypercontractivity for $1/2< p\\leq q < 1$ with explicit sufficient times. For each fixed $δ>0$, a sufficiently strong dephasing perturbation satisfies a uniform positive logarithmic Sobolev inequality on $[δ, 1]$ and hence quantum reverse hypercontractivity for $δ< p\\leq q<1$ with fixed $0<δ<1/2$. Furthermore, we establish reverse hypercontractivity for graph-based KMS-symmetric quantum Markov semigroups for $δ< p\\leq q< 1$ with fixed $0<δ<1$ for connected graphs when $n \\geq 3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00242",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinsong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fr0sv6n18eb9y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00242",
  "fulltext_url": null,
  "id": "fr0sv6n18eb9y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00242",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7215916818",
  "pdf_url": "https://arxiv.org/pdf/2610.00242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fr0sv6n18eb9y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantum Reverse Hypercontractivity for KMS-Symmetric Quantum Markov Semigroups",
  "title_text": "Quantum Reverse Hypercontractivity for KMS-Symmetric Quantum Markov Semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/fr0sv6n18eb9y",
  "venue": "arXiv",
  "versions": []
}