{
  "abstract": "We construct a dimension-dependent family of generalized equiangular measurements that gives explicit steering witnesses in every prime dimension $d\\geq5$. The construction consists of $d-1$ mutually unbiased measurements and an additional normalized family of $2d-1$ Hermitian operators depending on a parameter $τ$. Positivity of the latter family is the main technical problem. We show that the noncentral operators reduce to three-dimensional invariant blocks, while the remaining central operator is exactly solvable in a two-dimensional subspace. Two unitarily equivalent $3\\times3$ matrix representations describe the same active spectrum, but yield different Gershgorin enclosures because Gershgorin bounds are basis dependent. Combining the stronger endpoint from each representation gives a fully analytic asymmetric interval for $τ$ that guarantees a valid POVM. Combining this POVM with the $d-1$ MUMs yields an explicit GEAM. Finally, using a maximally entangled realization and the local-hidden-state bound previously derived for generalized equiangular measurements, we obtain an explicit steering inequality and a sufficient criterion guaranteeing quantum violation in every prime dimension $d\\geq5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07314",
  "author_total": 2,
  "authors": [
    {
      "name": "Adam Rutkowski"
    },
    {
      "name": "Katarzyna Siudzińska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fx9ch9c5he06.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07314",
  "fulltext_url": null,
  "id": "1fx9ch9c5he06",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07314",
  "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": "W7220972958",
  "pdf_url": "https://arxiv.org/pdf/2610.07314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fx9ch9c5he06.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07314"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Analytic construction of dimension-dependent steering witnesses from generalized equiangular measurements",
  "title_text": "Analytic construction of dimension-dependent steering witnesses from generalized equiangular measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/1fx9ch9c5he06",
  "venue": "arXiv",
  "versions": []
}