{
  "abstract": "We investigate the normalized operator geometry of the mixed Fibonacci–Lucas quaternion Qn = Fn + Lni + Fn+1j + Ln+1k. Standard quaternion representations associate this sequence with single-qubit unitary channels. We first establish a convergence theorem for quaternion sequences with two distinct real characteristic roots and a strictly dominant positive root. It gives an exact average gate infidelity to the limit and sharp projective-step asymptotics, including the degenerate constant-channel case. For the Fibonacci–Lucas assignment, orthogonal Binet coefficient vectors yield exact finite-index formulas with projective steps of order φ−2n and average gate infidelities of order φ−4n. Strict comparison of the five projective Clifford rotation classes proves that the limiting unitary has a unique nearest projective Clifford, the cyclic Pauli-axis permutation, with average gate fidelity 115+5/90≈0.884408. For the controlled family, product-input maximization gives concurrence 1−an2, while independent Haar averaging gives linear-entropy entangling power 21−an2/9. Both admit explicit algebraic limits. Reproducible matrix and high-precision scalar calculations verify these results. The analysis supplies exact convergence, finite-group, and entanglement benchmarks for a recurrence-indexed family without assuming Hamiltonian dynamics.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Science, Kastamonu University, 37100 Kastamonu, Türkiye",
    "Department of Biomedical Engineering, Faculty of Engineering and Architecture, Kastamonu University, 37100 Kastamonu, Türkiye"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zafer Ünal",
      "orcid": "0000-0003-2445-1028"
    },
    {
      "affs": [
        1
      ],
      "name": "Can Doğan Vurdu",
      "orcid": "0000-0002-5179-1266"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7745t4g8japs0.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203693",
  "fulltext_url": null,
  "id": "7745t4g8japs0",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3693",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221532037",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/7745t4g8japs0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203693",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Fibonacci–Lucas Recurrence-Indexed Quaternionic Unitaries: Channel Convergence, Clifford Proximity, and Controlled Entanglement",
  "title_text": "Fibonacci–Lucas Recurrence-Indexed Quaternionic Unitaries: Channel Convergence, Clifford Proximity, and Controlled Entanglement",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/7745t4g8japs0",
  "venue": "Mathematics",
  "versions": []
}