{
  "id": "1406.3537",
  "version": "v2",
  "published": "2014-06-13T13:57:06.000Z",
  "updated": "2014-10-01T09:45:19.000Z",
  "title": "Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures",
  "authors": [
    "G. M. Bosyk",
    "S. Zozor",
    "M. Portesi",
    "T. M. Osán",
    "P. W. Lamberti"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We provide a twofold extension of Landau--Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau--Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-13T13:57:06.000Z",
      "title": "Uncertainty relations à la Landau-Pollak for Positive Operator Valued Measures",
      "abstract": "We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for POVM sets, by recourse to geometric considerations. The generalization is based on distances between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such a distance plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from the Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation.",
      "comment": "11 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-01T09:45:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ca",
      "03.65.Ta",
      "02.50.-r",
      "05.90.+m"
    ],
    "keywords": [
      "positive operator valued measures",
      "landau-pollak uncertainty relations",
      "usual landau-pollak inequality",
      "twofold extension",
      "wootters metric"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevA.90.052114",
      "journal": "Physical Review A",
      "year": 2014,
      "month": "Nov",
      "volume": 90,
      "number": 5,
      "pages": "052114"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvA..90e2114B"
    }
  }
}