{
  "abstract": "We construct a nonlocal game that self-tests a maximally entangled qubit strategy among pure full-Schmidt-rank projective strategies, but admits an inequivalent optimum using one nonprojective measurement. This resolves a conjecture of Baptista et al. on imposing full rank and projectivity simultaneously. The construction combines CHSH with an auxiliary game $G$ that forces deterministic answers under these assumptions and admits a trine POVM optimum without them. We classify the optimal correlations of $G$ as a line segment parametrized by the tracial states of $\\mathbb{C}\\oplus M_2(\\mathbb{C})$. Projectivity on the state support removes the matrix summand, whereas projective dilations with nonzero nonabort probability have a nontracial local state whose zero left ideal is not two-sided. Finally, a family in local dimension six shows that the full-rank PVM self-test is not robust.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10013",
  "author_total": 1,
  "authors": [
    {
      "name": "Ranyiliu Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73s8xwvz5ks20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10013",
  "fulltext_url": null,
  "id": "73s8xwvz5ks20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10013",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212163305",
  "pdf_url": "https://arxiv.org/pdf/2609.10013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73s8xwvz5ks20.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10013"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Separation between Full-Rank PVM and Assumption-free Self-Testing",
  "title_text": "A Separation between Full-Rank PVM and Assumption-free Self-Testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/73s8xwvz5ks20",
  "venue": "arXiv",
  "versions": []
}