{
  "abstract": "We establish the exact exponent for smoothing the max-relative entropy on arbitrary von Neumann algebras. The proof first develops the required large-deviation and smoothing estimates in the semifinite setting and then passes to general von Neumann algebras through Haagerup-Junge-Xu reduction. We next study catalytic quantum information decoupling when the reference system is described by an arbitrary von Neumann algebra. A key ingredient is an operator layer-cake formula valid on arbitrary von Neumann algebras. This formula leads to a convex-split estimate for normal states with a general von Neumann algebraic reference system. Combining this estimate with the smoothing exponent result, we obtain lower and upper bounds on the catalytic-decoupling reliability function. These bounds coincide below the corresponding critical rate, yielding the exact decoupling reliability function in that regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07997",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiwen Lin"
    },
    {
      "name": "Hongsen Qiu"
    },
    {
      "name": "Xinyu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mddnbj6e9eez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07997",
  "fulltext_url": null,
  "id": "0mddnbj6e9eez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07997",
  "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.IT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7167888641",
  "pdf_url": "https://arxiv.org/pdf/2607.07997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mddnbj6e9eez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2607.07997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras",
  "title_text": "Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/0mddnbj6e9eez",
  "venue": "arXiv",
  "versions": []
}