{
  "abstract": "Self-testing certifies quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the spin representation of the continuous pin group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06755",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexander Kulpe"
    },
    {
      "name": "Giulio Malavolta"
    },
    {
      "name": "Simon Schmidt"
    },
    {
      "name": "Michael Walter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3dydntfgzp39.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06755",
  "fulltext_url": null,
  "id": "b3dydntfgzp39",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06755",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220745522",
  "pdf_url": "https://arxiv.org/pdf/2610.06755",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3dydntfgzp39.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06755",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06755"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Grothendieck Game and Self-Testing Continuous Groups",
  "title_text": "The Grothendieck Game and Self-Testing Continuous Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/b3dydntfgzp39",
  "venue": "arXiv",
  "versions": []
}