{
  "abstract": "The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, translation-invariant and gauge-invariant quasifree states on doubly infinite fermionic chains, and give explicit formulas for a wide range of regularized Rényi divergences between such states, including $(α,z)$, log-Euclidean, geometric, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and for any fixed $α$, the regularized Rényi $(α,z)$-divergences give different regularized values for different $z$ parameters in general. We also generalize a previous construction from [Bunth, Maróti, Mosonyi, Zimborás, Lett.~Math.~Phys.~113:(7), 2023] to the case of multiple modes per lattice site to obtain a large class of states exhibiting super-exponential decay of the discrimination error probabilities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.31379",
  "author_total": 2,
  "authors": [
    {
      "name": "Milán Mosonyi"
    },
    {
      "name": "Gábor Maróti-Zareczky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2k0xyywgenkk5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.31379",
  "fulltext_url": null,
  "id": "2k0xyywgenkk5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.31379",
  "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-ph"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7163017739",
  "pdf_url": "https://arxiv.org/pdf/2605.31379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2k0xyywgenkk5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2605.31379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.31379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rényi divergences and binary state discrimination error exponents for fermionic quasi-free states",
  "title_text": "Rényi divergences and binary state discrimination error exponents for fermionic quasi-free states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/2k0xyywgenkk5",
  "venue": "arXiv",
  "versions": []
}