{
  "id": "0909.4453",
  "version": "v2",
  "published": "2009-09-24T14:06:58.000Z",
  "updated": "2009-09-25T18:33:28.000Z",
  "title": "Classifying all mutually unbiased bases in Rel",
  "authors": [
    "Julia Evans",
    "Ross Duncan",
    "Alex Lang",
    "Prakash Panangaden"
  ],
  "comment": "11 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the categorical approach to quantum mechanics one can find examples of categories which behave ``like'' the category of finite-dimensional Hilbert spaces in various ways but are subtly different. One such category is the category of sets and relations, $\\mathbf{Rel}$. One can formulate the concept of mutually unbiased bases here as well. In this note we classify all the mutually unbiased bases in this category by relating it to a standard question in combinatorics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-25T18:33:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutually unbiased bases",
      "finite-dimensional hilbert spaces",
      "quantum information theory",
      "standard question",
      "quantum mechanics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4453E"
    }
  }
}