{
  "id": "1010.1335",
  "version": "v3",
  "published": "2010-10-07T04:37:00.000Z",
  "updated": "2011-06-27T05:05:42.000Z",
  "title": "Upper continuity bounds on the relative $q$-entropy for $q>1$",
  "authors": [
    "Alexey E. Rastegin"
  ],
  "comment": "7 pages, no figures. The statements and the proofs from Section III are corrected. The results of Section IV are improved. Appendix A has been excluded",
  "journal": "J. Math. Phys. 52, 062203 (2011)",
  "doi": "10.1063/1.3600535",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms of norm distances between its arguments are obtained in finite-dimensional context. These bounds characterize a continuity property in the sense of Fannes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-27T05:05:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ce",
      "03.65.Ta"
    ],
    "keywords": [
      "upper continuity bounds",
      "standard relative entropy",
      "upper bounds",
      "norm distances",
      "finite-dimensional context"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Jun",
      "volume": 52,
      "number": 6,
      "pages": 2203
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JMP....52f2203R"
    }
  }
}