{
  "id": "1304.7442",
  "version": "v2",
  "published": "2013-04-28T08:12:08.000Z",
  "updated": "2013-06-12T16:10:11.000Z",
  "title": "Von Neumann entropy and majorization",
  "authors": [
    "Yuan Li",
    "Paul Busch"
  ],
  "comment": "Version 2 contains some corrections and linguistic improvements",
  "journal": "Journal of Mathematical Analysis and Applications 408, 384-393 (2013)",
  "doi": "10.1016/j.jmaa.2013.06.019",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel $\\Phi$, one has $S(\\Phi(\\rho))=S(\\rho)$ for all quantum states $\\rho$ if and only if there exists an isometric operator $V$ such that $\\Phi(\\rho)=V\\rho V^*$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-12T16:10:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "von neumann entropy",
      "majorization",
      "infinite dimensional hilbert spaces",
      "probability distributions",
      "isometric operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7442L"
    }
  }
}