{
  "id": "math-ph/0701062",
  "version": "v3",
  "published": "2007-01-24T13:07:05.000Z",
  "updated": "2007-05-21T16:25:04.000Z",
  "title": "Uncertainty Principle and Quantum Fisher Information - II",
  "authors": [
    "P. Gibilisco",
    "D. Imparato",
    "T. Isola"
  ],
  "comment": "v2, Minor revision. v3, changes made to conform to version accepted on J. Math. Phys",
  "doi": "10.1063/1.2748210",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA"
  ],
  "abstract": "Heisenberg and Schr{\\\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\\rho}(A)\\cdot Var_{\\rho}(B)$, in a state $\\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not zero. In this paper we prove an uncertainty principle in Schr{\\\"o}dinger form where the bound for the product of variances $Var_{\\rho}(A)\\cdot Var_{\\rho}(B)$ depends on the area spanned by the commutators $[\\rho,A]$ and $[\\rho,B]$ with respect to an arbitrary quantum version of the Fisher information.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-05-21T16:25:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum fisher information",
      "uncertainty principle",
      "arbitrary quantum version",
      "commutator",
      "lower bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}