{
  "abstract": "We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\\exp(Θ_K(n^2))$, and \\[ χ(T_n^{\\otimes2})-2χ(T_n) \\ge n\\left[\\frac{\\log_2K}{K}-2\\log_2(1+9/K)\\right]-O(1/n). \\] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates. We also provide a Lean certificate for our proofs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18222",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinzhao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brqwar853wz70.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18222",
  "fulltext_url": null,
  "id": "brqwar853wz70",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18222",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213523925",
  "pdf_url": "https://arxiv.org/pdf/2609.18222",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brqwar853wz70.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.18222",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18222"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Unbounded Holevo additivity gaps in finite dimensions",
  "title_text": "Unbounded Holevo additivity gaps in finite dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/brqwar853wz70",
  "venue": "arXiv",
  "versions": []
}