{
  "abstract": "We characterize the exact error-exponent trade-off in binary quantum hypothesis testing with a rejection option for faithful states on a finite-dimensional Hilbert space. The probabilities of rejection under the two hypotheses are required to vanish exponentially, with exponents at least $K$ and $L$. We show that a quadruple $(a,b,K,L)$ of positive error and rejection exponents is achievable if and only if it satisfies three single-letter conditions: two conditions involve Petz--Rényi quantities and coincide with the converse bound conjectured to be tight by Ji and Regula; the third involves the $α$--$z$ Rényi quantities on the triangle $\\max\\{α,1-α\\}\\le z\\le1$. The proof combines a sector decomposition inside Schur--Weyl blocks, an explicit one-shot measurement construction, and an exact minimax argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00931",
  "author_total": 1,
  "authors": [
    {
      "name": "Yonglong Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3am4memf7w0a8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00931",
  "fulltext_url": null,
  "id": "3am4memf7w0a8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00931",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3am4memf7w0a8.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Binary Quantum Hypothesis Testing with a Rejection Option: The Exact Error-Exponent Trade-off",
  "title_text": "Binary Quantum Hypothesis Testing with a Rejection Option: The Exact Error-Exponent Trade-off",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3am4memf7w0a8",
  "venue": "arXiv",
  "versions": []
}