{
  "abstract": "How much entanglement can two distant laboratories share when their connection is noisy? We relate this question to deciding which of two quantum hypotheses is present. Our one-shot bounds apply to entanglement generation over a quantum channel and to one-way entanglement distillation from a shared state. We use Cheng's trace inequality to bound the infidelity of a Petz decoder in terms of a binary hypothesis testing cost. Applying the inequality before averaging over codes reduces the error analysis to computing a second moment of random subspaces. The proof covers every integer target dimension and treats rank-deficient states explicitly. A corollary expresses the achievable entanglement through hypothesis-testing coherent information, with a single logarithmic error slack and exact integer rounding. We also prove an error-preserving conversion from entanglement generation codes to entanglement transmission codes: the target dimension decreases by only a constant factor at fixed error, and the decoder is the original decoder followed by local processing. Consequently, for both entanglement generation and entanglement transmission, arbitrary pure reference-input states yield the same coherent-information rate, second-order Gaussian correction at the original error tolerance, and explicit achievable logarithmic remainder. For commuting testing hypotheses, the logarithmic remainder improves to a constant. These results give a direct route from binary distinguishability to explicit recovery guarantees and finite-resource quantum communication rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31501",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew Can"
    },
    {
      "name": "Mark M. Wilde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/391beyx1waatp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31501",
  "fulltext_url": null,
  "id": "391beyx1waatp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31501",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7223312032",
  "pdf_url": "https://arxiv.org/pdf/2610.31501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/391beyx1waatp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "One-shot entanglement generation and distillation via Petz recovery and binary hypothesis testing",
  "title_text": "One-shot entanglement generation and distillation via Petz recovery and binary hypothesis testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/391beyx1waatp",
  "venue": "arXiv",
  "versions": []
}