{
  "id": "quant-ph/0409184",
  "version": "v2",
  "published": "2004-09-27T14:28:41.000Z",
  "updated": "2004-11-25T10:58:27.000Z",
  "title": "Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?",
  "authors": [
    "Metod Saniga",
    "Michel Planat"
  ],
  "comment": "3 pages, no figures",
  "journal": "Chaos, Solitons and Fractals 26 (2005) 1267 - 1270",
  "categories": [
    "quant-ph"
  ],
  "abstract": "This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an analogue of an arc in a (Desarguesian) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two principally distinct kinds of ovals for d even and greater than four, viz. conics and non-conics, implies the existence of two qualitatively different groups of the complete sets of MUBs for the Hilbert spaces of corresponding dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-25T10:58:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutually unbiased bases",
      "finite projective planes",
      "complete sets",
      "d-dimensional hilbert space",
      "quantum semiclass"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.chaos.2005.03.008",
      "journal": "Chaos Solitons and Fractals",
      "year": 2005,
      "month": "Dec",
      "volume": 26,
      "number": 5,
      "pages": 1267
    },
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005CSF....26.1267S"
    }
  }
}