{
  "id": "quant-ph/0410045",
  "version": "v1",
  "published": "2004-10-06T13:33:09.000Z",
  "updated": "2004-10-06T13:33:09.000Z",
  "title": "On the 'Polarized distances between quantum states and observables'",
  "authors": [
    "D. A. Trifonov"
  ],
  "comment": "6 pages, Latex, 2 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The scheme for construction of distances, presented in the previous paper quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of Ref. 1 does not ensure the triangle inequality, therefore some of the functionals D(a,b) in Ref. 1 are in fact quasi-distances. In this note we formulate sufficient conditions for a functional D(a,b) of the (squared) form D(a,b)^2 = f(a)^2 + f(b)^2 - 2f(a)f(b)g(a,b) to be a distance and provide some examples of such distances. A one parameter generalization of a bounded distance of the (squared) form D(a,b)^2 = D_0^2 (1 - g(a,b)), which includes the known Bures-Uhlmann and Hilbert-Schmidt distances between quantum states, is established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-06T13:33:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum states",
      "polarized distances",
      "observables",
      "formulate sufficient conditions",
      "parameter generalization"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph.10045T"
    }
  }
}