{
  "abstract": "We investigate converse bounds on the average decoding error probability in finite-blocklength classical-quantum channel coding. We first present a lower bound for multiple quantum hypothesis testing in terms of pairwise trace distances and derive a corresponding fidelity bound. We then obtain a spectrum-based converse that depends only on the a priori probabilities and spectra of the states. We show that the converse bound remains tight for the quantum depolarizing channel under suitable conditions. For codes with product-state outputs, this converse takes an explicit form involving products of output-state eigenvalues. We apply it to binary codes over the quantum amplitude damping channel using the input states $\\vert+\\rangle$ and $\\vert-\\rangle$. For this setting, we also discuss a normal approximation to the spectrum-based converse in the large blocklength regime. In all numerical examples considered, the spectrum-based converse is tighter than the other converse bounds at low noise levels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06840",
  "author_total": 3,
  "authors": [
    {
      "name": "Tam{á}s Havas"
    },
    {
      "name": "Hsuan-Yin Lin"
    },
    {
      "name": "Eirik Rosnes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fsqq44f1gtbw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06840",
  "fulltext_url": null,
  "id": "2fsqq44f1gtbw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06840",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220650557",
  "pdf_url": "https://arxiv.org/pdf/2610.06840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fsqq44f1gtbw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:05Z",
      "native_id": "2610.06840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding",
  "title_text": "A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2fsqq44f1gtbw",
  "venue": "arXiv",
  "versions": []
}