{
  "abstract": "For a collection of states indexed by $[n]={1,\\ldots,n}$, let $F(H)$ denote the optimal unnormalized minimum discrimination error for each nonempty subfamily $H\\subseteq[n]$. We call $F$ the discrimination profile and characterize exactly which profiles can arise in a general probabilistic theory (GPT). For fixed $n$, the GPT region $\\mathfrak{G}_n$ is a bounded rational polytope, giving a hierarchy $\\mathfrak{C}_n\\subseteq\\mathfrak{Q}_n\\subseteq\\mathfrak{G}_n$ of classical, quantum, and GPT profiles, analogous to the local--quantum--no-signalling hierarchy in Bell theory. For $n=3$ we determine the classical and GPT polytopes explicitly. Within $\\mathfrak{G}_3$, the classical region is characterized by $β:=F(123)-F(12)-F(13)-F(23)\\le0$, while the GPT maximum is $1$. For qubit triples, the maximal value is attained by the trine, $β_{\\mathrm{tr}}=3\\sqrt3/2-2$, and we prove the dimension-independent quantum bound $β_{\\mathrm Q}\\le2/3$, with a slight further improvement. Hence $0=β_{\\mathrm C}<3\\sqrt3/2-2\\leβ_{\\mathrm Q}\\le2/3<1=β_{\\mathrm{GPT}}$. We conjecture $β_{\\mathrm Q}=β_{\\mathrm{tr}}$ and prove this for arbitrary pure-state triples, together with further supporting evidence. For arbitrary $n$, every classical facet admitting a GPT violation already admits a quantum violation in dimension at most $3$. A four-state qubit example shows that quantum success profiles need not be submodular, unlike for $n=3$. Finally, we exhibit a four-dimensional quantum triple whose discrete profile is classical for all subfamilies but becomes nonclassical when unequal priors are allowed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17920",
  "author_total": 1,
  "authors": [
    {
      "name": "Mihály Weiner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpgzrgvp7xga8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17920",
  "fulltext_url": null,
  "id": "cpgzrgvp7xga8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17920",
  "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.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7213503589",
  "pdf_url": "https://arxiv.org/pdf/2609.17920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpgzrgvp7xga8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.17920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Classical, quantum, and general probabilistic state-discrimination profiles",
  "title_text": "Classical, quantum, and general probabilistic state-discrimination profiles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/cpgzrgvp7xga8",
  "venue": "arXiv",
  "versions": []
}