{
  "abstract": "We give a closed-form finite-dimensional construction of quantum channels with real algebraic entries exhibiting arbitrarily large violations of minimum-output Rényi entropy additivity uniformly above any prescribed positive Rényi order, using a different finite realization based on direct products of free groups and fixed-field high-girth graphs. More precisely, for every $p_0>0$ and $g>0$, we construct one channel and one Bell input for which the additivity gap is greater than $g$ simultaneously for all $p\\in[p_0,\\infty]$. With $r=\\lceil2g\\rceil$, the construction uses $15r$ output qubits and $O(r2^{30r}+r^2(1+p_0^{-1}))$ input qubits. Compared with the stated parameters of Shou and Gorshkov \\cite{ShouGorshkov2026}, our construction uses fewer output qubits for every target gap and has a smaller asymptotic input-qubit bound as the gap grows with the positive cutoff fixed. At the von Neumann order, a separate specialization gives an explicit channel with gap greater than $1/1024$ using $37608898$ input qubits and $8$ output qubits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06533",
  "author_total": 3,
  "authors": [
    {
      "name": "Guocheng Zhen"
    },
    {
      "name": "Ranyiliu Chen"
    },
    {
      "name": "Xin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ec6pe0bcqn320.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06533",
  "fulltext_url": null,
  "id": "ec6pe0bcqn320",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06533",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220705461",
  "pdf_url": "https://arxiv.org/pdf/2610.06533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ec6pe0bcqn320.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06533"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Closed-Form Arbitrary-Gap Rényi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs",
  "title_text": "Closed-Form Arbitrary-Gap Rényi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/ec6pe0bcqn320",
  "venue": "arXiv",
  "versions": []
}