{
  "annotation_id": "5849b0a6-bac1-4c03-92d0-778b8de6a6cf",
  "date_created": "2026-03-02T18:02:09.452000Z",
  "date_modified": "2026-03-02T18:02:09.452000Z",
  "file_hash": "28618626d61991026ff6d13ebd32a38d4c194055d042422b4eba29c06c424f77",
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  "record": {
    "abstract": "This note is a short elaboration of the conjecture of Saniga et al (J. Opt.\nB: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased\nbases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as\nan analogue of an arc in a (Desarguesian) projective plane of order d. Complete\nsets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two\nprincipally distinct kinds of ovals for d even and greater than four, viz.\nconics and non-conics, implies the existence of two qualitatively different\ngroups of the complete sets of MUBs for the Hilbert spaces of corresponding\ndimensions.",
    "arxiv_id": "quant-ph/0409184",
    "authors": [
      "Metod Saniga",
      "Michel Planat"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/j.chaos.2005.03.008",
    "journal_ref": "Chaos, Solitons and Fractals 26 (2005) 1267 - 1270",
    "title": "Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?",
    "url": "https://arxiv.org/abs/quant-ph/0409184"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3eebe646-c711-4e1a-875a-83919631195f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}