{
  "abstract": "We present a generalization of the Mermin-Peres magic square game to $N$ players, in which the square is replaced by an $N$-dimensional hypercube. We show that the winning probability of the optimal classical strategy remains $8/9$ for all $N$, while for $N \\ge 3$, a generalization of the quantum strategy for $N = 2$ achieves a winning probability between $1/3$ and $3/4$. This loss of quantum advantage for $N \\ge 3$ is a consequence of monogamy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06534",
  "author_total": 2,
  "authors": [
    {
      "name": "Itamar Lorian"
    },
    {
      "name": "J. E. Avron"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94y8zdpqddtrv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06534",
  "fulltext_url": null,
  "id": "94y8zdpqddtrv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06534",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220693601",
  "pdf_url": "https://arxiv.org/pdf/2610.06534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94y8zdpqddtrv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.06534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06534"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Mermin-Peres Magic Square Game With Three or More Players",
  "title_text": "The Mermin-Peres Magic Square Game With Three or More Players",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/94y8zdpqddtrv",
  "venue": "arXiv",
  "versions": []
}