{
  "id": "quant-ph/0103162",
  "version": "v3",
  "published": "2001-03-29T18:55:41.000Z",
  "updated": "2001-09-07T23:59:06.000Z",
  "title": "A new proof for the existence of mutually unbiased bases",
  "authors": [
    "Somshubhro Bandyopadhyay",
    "P. Oscar Boykin",
    "Vwani Roychowdhury",
    "Farrokh Vatan"
  ],
  "comment": "Revised version. To appear in the special issue of Algorithmica on Quantum Algorithms and Quantum Cryptography",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2^m.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-09-07T23:59:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutually unbiased bases",
      "orthogonal unitary matrices",
      "pauli matrices",
      "finite dimension",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001quant.ph..3162B"
    }
  }
}