{
  "abstract": "We extend the three-state overlap analysis to determine the exact quantum maximum over finite-dimensional pure-state realizations of the $n$-cycle overlap inequalities, $S_n^{\\max}=n\\cos^2(π/(2n))-1$, for arbitrary cycle length $n\\ge3$. The bound is saturated by an explicit family of coplanar qubit states equally spaced along a Fubini--Study geodesic, establishing dimensional saturation of the overlap-cycle hierarchy. Thus, the global optimum over all finite-dimensional pure-state realizations is already achieved in dimension two. We further show how, under ideal symmetric interferometric conditions, the overlap quantities can be inferred from pairwise fringe visibilities. The three-state case recovers the known maximum $5/4$, while the exact $n$-cycle result shows that the quantum--classical gap approaches one as $n\\to\\infty$, with corresponding visibility thresholds. Within generalized noncontextuality frameworks, and subject to the required operational equivalences, such violations can witness preparation contextuality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.14395",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohd Asad Siddiqui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ejw1mw9w3js9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14395",
  "fulltext_url": null,
  "id": "6ejw1mw9w3js9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14395",
  "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": "W7161302205",
  "pdf_url": "https://arxiv.org/pdf/2605.14395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ejw1mw9w3js9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2605.14395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14395"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Quantum Maxima of the $n$-Cycle Overlap Inequalities",
  "title_text": "Exact Quantum Maxima of the n-Cycle Overlap Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/6ejw1mw9w3js9",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1098/rspa.2026.0596",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}