{
  "id": "0804.2193",
  "version": "v2",
  "published": "2008-04-14T14:44:45.000Z",
  "updated": "2009-01-19T07:44:00.000Z",
  "title": "Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models",
  "authors": [
    "Tomasz Paterek",
    "Borivoje Dakic",
    "Caslav Brukner"
  ],
  "comment": "Published version",
  "journal": "Phys. Rev. A 79, 012109 (2009)",
  "doi": "10.1103/PhysRevA.79.012109",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-19T07:44:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ta",
      "02.10.Ox"
    ],
    "keywords": [
      "mutually unbiased bases",
      "hidden-variable models",
      "complementary quantum measurements",
      "mutually orthogonal latin squares",
      "unbiased bases encapsulate"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2009,
      "month": "Jan",
      "volume": 79,
      "number": 1,
      "pages": "012109"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvA..79a2109P"
    }
  }
}