{
  "abstract": "A key goal in the foundations of quantum mechanics is to identify operational constraints characterizing physical theories. Bell inequalities do so for classical probability theory, while Tsirelson's bound provides a first step for quantum mechanics. Here, we address the dual question: Can one certify that all correlations predicted by quantum theory are actually realizable? In this work, we construct a finite number of two-body correlations such that the only probabilistic theory that (1) realizes them, and (2) does so in a way that is stable under iterated teleportation, is quantum theory. For $n$ quantum systems of dimension $d$ each, Condition (1) can be verified using $\\operatorname{poly}(d,n)$ measurement settings. Condition (2) may be understood as a hierarchy of tests, one for each number $N$ of teleportation steps. There is thus a sense in which finite-dimensional quantum theory can be self-tested. In particular, one can certify the existence of Bell inequality violations larger than any that have been directly observed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03694",
  "author_total": 4,
  "authors": [
    {
      "name": "Lionel J. Dmello"
    },
    {
      "name": "Xiangling Xu"
    },
    {
      "name": "Marc-Olivier Renou"
    },
    {
      "name": "David Gross"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eqfkcfevft6k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03694",
  "fulltext_url": null,
  "id": "5eqfkcfevft6k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03694",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7220372882",
  "pdf_url": "https://arxiv.org/pdf/2610.03694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eqfkcfevft6k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.03694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03694"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "An operational characterization of finite-dimensional quantum theory",
  "title_text": "An operational characterization of finite-dimensional quantum theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/5eqfkcfevft6k",
  "venue": "arXiv",
  "versions": []
}