{
  "id": "math-ph/0407007",
  "version": "v2",
  "published": "2004-07-06T09:18:29.000Z",
  "updated": "2004-10-08T13:33:27.000Z",
  "title": "On the monotonicity of scalar curvature in classical and quantum information geometry",
  "authors": [
    "P. Gibilisco",
    "T. Isola"
  ],
  "comment": "20 pages, 2 .eps figures; (v2) section 2 rewritten, typos corrected",
  "doi": "10.1063/1.1834693",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries and Wigner-Yanase-Dyson information. Finally we show that this last conjecture implies the truth of the Petz conjecture about the monotonicity of the scalar curvature of the Bogoliubov-Kubo-Mori monotone metric.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-08T13:33:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum information geometry",
      "scalar curvature",
      "monotonicity",
      "bogoliubov-kubo-mori monotone metric",
      "quantum alpha-geometries"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}