{
  "annotation_id": "e55ef328-5a5c-443e-b926-862623a35646",
  "date_created": "2026-03-02T18:02:34.237000Z",
  "date_modified": "2026-03-02T18:02:34.237000Z",
  "file_hash": "85f8cfb0ebffa3f52aa6a2e4a4f9aa6f0d3661799d5a24c332a0b3968f2cf998",
  "private": false,
  "record": {
    "abstract": "The question of determining the maximal number of mutually unbiased bases in\ndimension six has received much attention since their introduction to quantum\ninformation theory, but a definitive answer has still not been found. In this\npaper we move away from the traditional analytic approach and use a numerical\napproach to attempt to determine this number. We numerically minimise a\nnon-negative function of a set of N+1 orthonormal bases in dimension d which\nonly evaluates to zero if the bases are mutually unbiased. As a result we find\nstrong evidence that (as has been conjectured elsewhere) there are no more than\nthree mutually unbiased bases in dimension six.",
    "arxiv_id": "quant-ph/0701122",
    "authors": [
      "Paul Butterley",
      "William Hall"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/j.physleta.2007.04.059",
    "title": "Numerical evidence for the maximum number of mutually unbiased bases in   dimension six",
    "url": "https://arxiv.org/abs/quant-ph/0701122"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eb5d9d77-b514-4341-8392-162c806cd07f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}