{
  "abstract": "We show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation. Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25117",
  "author_total": 2,
  "authors": [
    {
      "name": "Ranyiliu Chen"
    },
    {
      "name": "Yuming Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbfrs6mjhfw18.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25117",
  "fulltext_url": null,
  "id": "dbfrs6mjhfw18",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25117",
  "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",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214105674",
  "pdf_url": "https://arxiv.org/pdf/2609.25117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbfrs6mjhfw18.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2609.25117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A non-robust quantum correlation self-test",
  "title_text": "A non-robust quantum correlation self-test",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/dbfrs6mjhfw18",
  "venue": "arXiv",
  "versions": []
}