{
  "id": "1006.3614",
  "version": "v2",
  "published": "2010-06-18T06:20:04.000Z",
  "updated": "2011-07-06T07:47:29.000Z",
  "title": "Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices",
  "authors": [
    "H. F. Chau"
  ],
  "comment": "13 pages in RevTex 4.1, 2 figures, to appear in QIC. This replacement concentrates only on the more physics and quantum information aspects of the results reported in the original manuscript with a more detailed proof. The mathematical results involving the discovery of several matrix inequalities reported in the original version will be strengthened and rewritten in a separate posting",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found. Interestingly, this family of metrics can be naturally converted into useful indicators of the degree of non-commutativity between two unitary matrices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-06T07:47:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary matrices",
      "non-commutativity",
      "application",
      "quantifying",
      "minimum resources"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.3614C"
    }
  }
}