{
  "abstract": "We present two results derived from the sharp log-Sobolev inequality for the uniform measure on a complete graph which concern the von Neumann entropy and the Entanglement of Formation of a state of finite and infinite-dimensional quantum systems. The first result is a sharp Lipschitz lower semicontinuity bound for the von Neumann entropy at any mixed state $ρ$ with uniform positive spectrum (i.e. a state proportional to a projector) w.r.t. the fidelity deficit: the inequality $\\,S(ρ)-S(σ)\\leq C_ρ(1-F(ρ,σ))\\,$ valid for any state $σ$, where $C_ρ$ is a constant depending on the rank of $ρ$. The second result is a sharp Lipschitz lower semicontinuity bound for the Entanglement of Formation at any pure state $ρ$ with uniform positive spectrum of marginal states w.r.t. the fidelity deficit: the inequality $\\,E_F(ρ)-E_F(σ)\\leq C_ρ(1-\\mathrm{Tr}ρσ)\\,$ valid for any state $σ$, where $C_ρ$ is a constant depending on the Schmidt rank of $ρ$. In both cases the optimal constant $C_ρ$ is equal to the optimal constant $K_{d}$ in the log-Sobolev inequality for the complete graph with $d$ vertices: in the first case $d=\\mathrm{rank}ρ$, in the second one $d=\\mathrm{rank}ρ_A=\\mathrm{rank}ρ_B$. The authors are grateful to GPT 5.6 for valuable discussion and technical help in preparing this note.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12667",
  "author_total": 2,
  "authors": [
    {
      "name": "A. S. Holevo"
    },
    {
      "name": "M. E. Shirokov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7ry58egf28cn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12667",
  "fulltext_url": null,
  "id": "b7ry58egf28cn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12667",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.IT"
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      "arxiv",
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      "arxiv",
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    [
      "openalex",
      "1702|Quantum Information and Cryptography"
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  "openalex": "W7212492655",
  "pdf_url": "https://arxiv.org/pdf/2609.12667",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7ry58egf28cn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.12667",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12667"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Log-Sobolev inequality, von Neumann entropy and Entanglement of Formation",
  "title_text": "Log-Sobolev inequality, von Neumann entropy and Entanglement of Formation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/b7ry58egf28cn",
  "venue": "arXiv",
  "versions": []
}