{
  "abstract": "We prove an integral representation of the $α$-$z$ Rényi divergences for normal states on arbitrary von Neumann algebras. Along each ray $z=cα$, the divergence is a positive average of relative entropies evaluated in a canonical family of escort states. For orders $α$ above one, we require the divergence to be finite, whereas for orders below one support inclusion suffices. An explicit boundary correction removes the lower-order support assumption. The proof uses a compatible weighted Haagerup $L^p$ scale and applies outside the data-processing region. For faithful density matrices, we express the derivative of the escort relative entropy with respect to the Rényi order in terms of a nonnegative fluctuation quantity. Differences of order-one derivatives of the divergence give quantum Fisher information and Wigner-Yanase skew information. For faithful bipartite density matrices, we also express optimized conditional $α$-$z$ entropies at orders above one as averages of ordinary conditional entropies. Further applications concern coherent-state divergences in quantum field theory and the optimizing order for the strong converse exponent in hypothesis-testing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21214",
  "author_total": 2,
  "authors": [
    {
      "name": "Tanay Kibe"
    },
    {
      "name": "Pratik Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ac95282p47j5z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21214",
  "fulltext_url": null,
  "id": "ac95282p47j5z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21214",
  "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",
      "hep-th"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.MP"
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    [
      "arxiv",
      "math.OA"
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      "openalex",
      "2604|Mathematical Inequalities and Applications"
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  "openalex": "W7204087035",
  "pdf_url": "https://arxiv.org/pdf/2608.21214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ac95282p47j5z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2608.21214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Integral representations of quantum Rényi divergences on von Neumann algebras",
  "title_text": "Integral representations of quantum Rényi divergences on von Neumann algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ac95282p47j5z",
  "venue": "arXiv",
  "versions": []
}