{
  "abstract": "We investigate restrictions on the dimensions and coordinate fields of real Weyl-Heisenberg fiducial vectors. Our main result is that such vectors can exist only in dimensions $d\\equiv 3\\pmod{4}$. This result is motivated by evidence showing that real Weyl-Heisenberg fiducial vectors can exist only in dimensions $d = 4m^2 + 3, m \\in \\mathbb{Z}_{\\geq 0}$. We further restrict the possible dimensions when the coordinate field is a totally real number field, an even or odd degree extension of $\\mathbb{Q}$, a real quadratic field, or a maximal real subfield of a cyclotomic field. Lastly, we establish non-existence over odd-degree number fields under either positivity of all non-trivial cyclic-shift overlaps or a conjectural containment of a distinguished quadratic field in the SIC field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13168",
  "author_total": 2,
  "authors": [
    {
      "name": "Igor Van Loo"
    },
    {
      "name": "Frédérique Oggier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/859j173j0g3v3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13168",
  "fulltext_url": null,
  "id": "859j173j0g3v3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13168",
  "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",
      "math.NT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7221567994",
  "pdf_url": "https://arxiv.org/pdf/2610.13168",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/859j173j0g3v3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.13168",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13168"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Real Fiducial Vectors Only Exist in Dimensions $d\\equiv 3 \\pmod{4}$",
  "title_text": "Real Fiducial Vectors Only Exist in Dimensions d≡ 3 pmod4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/859j173j0g3v3",
  "venue": "arXiv",
  "versions": []
}