{
  "abstract": "Quantum measurements can exhibit contextuality: their outcomes cannot always be explained by assigning pre-existing values that are independent of which compatible measurements are performed together. The Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality provides the canonical minimal test of this effect for a single three-level quantum system, or qutrit, using five measurement events arranged as a pentagon. Here we ask whether a larger but still compact set of measurement events can produce a stronger separation between quantum predictions and the corresponding noncontextual limit. We perform an exhaustive search over all 11,117 connected non-isomorphic graphs with eight vertices, where each vertex represents a measurement event and edges connect pairs of events that cannot occur together. We identify a sparse ten-edge graph, which we call Quad-$C_5$, as the unique maximizer of this separation at the reported numerical precision. The graph can be understood as four overlapping KCBS pentagons, with every edge shared by two pentagons. Quad-$C_5$ already demonstrates contextuality in a qutrit, for which we obtain an exact analytical result and find the same violation above the noncontextual bound as in the original KCBS test. The larger quantum-noncontextual separation allowed by the graph, however, becomes accessible in a four-level quantum system, where numerical optimization reaches the full graph-theoretic quantum bound and yields a larger contextuality gap than the standard eight-vertex Wagner-graph benchmark while requiring fewer pairwise constraints. Quad-$C_5$ therefore provides a compact connection between minimal qutrit contextuality and stronger contextuality tests available in higher-dimensional quantum systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12828",
  "author_total": 5,
  "authors": [
    {
      "name": "Uğur Tamer"
    },
    {
      "name": "Berke Ünal"
    },
    {
      "name": "Alper Dizdar"
    },
    {
      "name": "Zafer Gedik"
    },
    {
      "name": "Özgür E. Müstecaplıoğlu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4n86cjayrdw2z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12828",
  "fulltext_url": null,
  "id": "4n86cjayrdw2z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12828",
  "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": "W7161172914",
  "pdf_url": "https://arxiv.org/pdf/2605.12828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4n86cjayrdw2z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2605.12828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12828"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Quad-$C_5$ Graph: Maximum Contextuality Gap on Eight Vertices",
  "title_text": "The Quad-C_5 Graph: Maximum Contextuality Gap on Eight Vertices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/4n86cjayrdw2z",
  "venue": "arXiv",
  "versions": []
}