{
  "abstract": "We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via convex generators and establish a duality theory yielding proper quantum scoring rules using McCarthy's tangent-plane construction. We derive local minimax optimal bounds for quantum state tomography under these incentives, proving a Local Holevo-McCarthy Bound that explicitly links asymptotic risk to the Bogoliubov-Kubo-Mori metric and the Holevo bound. Furthermore, we establish an exact coherence floor that quantifies the irreducible excess score of fixed-basis forecasting strategies when phases are unknown (minimax over the phase orbit), proving a worst-case minimax floor of $\\log d$ over the full state space. Our results contextualize fundamental sample complexity separations compared to optimal quantum estimation strategies and guide the design of incentive-compatible quantum data markets and robust quantum machine learning protocols.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.05268",
  "author_total": 1,
  "authors": [
    {
      "name": "M. W. AlMasri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fk7nmw2kfky2m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.05268",
  "fulltext_url": null,
  "id": "fk7nmw2kfky2m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.05268",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7160616137",
  "pdf_url": "https://arxiv.org/pdf/2605.05268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fk7nmw2kfky2m.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:58Z",
      "native_id": "2605.05268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.05268"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Proper Scoring Rules: Convex Duality, Bregman Risk, and the Coherence Gap",
  "title_text": "Quantum Proper Scoring Rules: Convex Duality, Bregman Risk, and the Coherence Gap",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/fk7nmw2kfky2m",
  "venue": "arXiv",
  "versions": []
}