{
  "id": "quant-ph/0701122",
  "version": "v2",
  "published": "2007-01-17T16:00:19.000Z",
  "updated": "2007-03-13T12:03:36.000Z",
  "title": "Numerical evidence for the maximum number of mutually unbiased bases in dimension six",
  "authors": [
    "Paul Butterley",
    "William Hall"
  ],
  "comment": "4 pages, 2 figures, some minor changes made",
  "doi": "10.1016/j.physleta.2007.04.059",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper we move away from the traditional analytic approach and use a numerical approach to attempt to determine this number. We numerically minimise a non-negative function of a set of N+1 orthonormal bases in dimension d which only evaluates to zero if the bases are mutually unbiased. As a result we find strong evidence that (as has been conjectured elsewhere) there are no more than three mutually unbiased bases in dimension six.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-13T12:03:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutually unbiased bases",
      "maximum number",
      "numerical evidence",
      "traditional analytic approach",
      "quantum information theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}