{
  "id": "0904.1963",
  "version": "v3",
  "published": "2009-04-13T16:22:58.000Z",
  "updated": "2009-11-17T11:45:36.000Z",
  "title": "Continuity of the von Neumann entropy",
  "authors": [
    "M. E. Shirokov"
  ],
  "comment": "42 pages, the minor changes have been made, the new applications of the continuity condition have been added. To appear in Commun. Math. Phys",
  "journal": "Commun. Math. Phys., vol. 296, no. 3, 625-654 (2010).",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and to obtain several new conditions. The method is based on a particular approximation of the von Neumann entropy by an increasing sequence of concave continuous unitary invariant functions defined using decompositions into finite rank operators. The existence of this approximation is a corollary of a general property of the set of quantum states as a convex topological space called the strong stability property. This is considered in the first part of the paper.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-17T11:45:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "von neumann entropy",
      "continuity",
      "concave continuous unitary invariant functions",
      "strong stability property"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "doi": "10.1007/s00220-010-1007-x",
      "year": 2010,
      "month": "Jun",
      "volume": 296,
      "number": 3,
      "pages": 625
    },
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010CMaPh.296..625S"
    }
  }
}