{
  "abstract": "We study planar openbooks obtained by lifting braids through branched covers of D^2, together with the quantum operations in the Ising representation. We give a criterion for the Stein fillings to be Calabi-Yau (CY). Among positive factorizations of a fixed monodromy, a CY one has minimal length and its filling minimizes χand b_2. Applied to Baykur's recent examples, this gives a planar contact 3-manifold with infinitely many non-homeomorphic CY fillings, the cover there having degree \\ge 6. At degree 4 a single CY filling forces every filling to be CY, and in one case the filling is unique; at degree \\le 3 it is unique, and CY under a mild condition. Admissible cuts of D^2 decompose the openbook into subopenbooks. Every positive factorization then localizes, and the CY condition holds exactly when it holds locally. The state space is then a direct sum of tensor products indexed by the compatible parity choices, with at most two qubits per factor when the pieces have degree $\\le 4$, the same range in which the CY condition depends only on the monodromy. For one degree 4 cover, the points, lines and flags of the two-qubit doily are realized by its subopenbooks. Fifteen liftable braids there share the same quantum operation and Stein filling, and are separated only by the subopenbook systems they admit. A choice of tensor-product structure is thus carried by the lift, not by the braid group representation, suggesting a link between contact topology and quantum entanglement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30406",
  "author_total": 1,
  "authors": [
    {
      "name": "Atsuhide Mori"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77c8yvckdmncq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30406",
  "fulltext_url": null,
  "id": "77c8yvckdmncq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30406",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.SG"
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      "arxiv",
      "quant-ph"
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7214676777",
  "pdf_url": "https://arxiv.org/pdf/2609.30406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77c8yvckdmncq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.30406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Planar Contact Structures with Calabi-Yau Fillings and Topological Quantum Computation",
  "title_text": "Planar Contact Structures with Calabi-Yau Fillings and Topological Quantum Computation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/77c8yvckdmncq",
  "venue": "arXiv",
  "versions": []
}