{
  "abstract": "We propose a new method for proving $L^2$ and modified logarithmic Sobolev inequalities with constants independent of system size for quantum Gibbs samplers whose Lindblad generators satisfy Kubo-Martin-Schwinger (KMS) detailed balance. We first establish the $L^2$ logarithmic Sobolev inequality by transporting it along a temperature-dependent path from the infinite-temperature product state to the target Gibbs state while maintaining a size-independent decay rate for the sandwiched Rényi-2 divergence. A tensor-power argument, combined with the quantum asymptotic equipartition property, then transfers this decay bound to relative entropy, yielding the modified logarithmic Sobolev inequality. This approach provides a general framework for proving size-independent logarithmic Sobolev inequalities for quantum Gibbs samplers. We apply it to two regimes: one-dimensional quantum spin chains at every finite temperature, and finite-range quantum spin systems at sufficiently high temperature in any fixed dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31571",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongrui Chen"
    },
    {
      "name": "Zhiyan Ding"
    },
    {
      "name": "Jianfeng Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zyzzb336yky6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31571",
  "fulltext_url": null,
  "id": "1zyzzb336yky6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31571",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223334580",
  "pdf_url": "https://arxiv.org/pdf/2610.31571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zyzzb336yky6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers",
  "title_text": "Size-independent Logarithmic Sobolev Inequalities for Quantum Gibbs Samplers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1zyzzb336yky6",
  "venue": "arXiv",
  "versions": []
}