{
  "id": "1102.3041",
  "version": "v2",
  "published": "2011-02-15T11:31:16.000Z",
  "updated": "2011-04-27T09:58:40.000Z",
  "title": "Telescopic Relative Entropy--II Triangle inequalities",
  "authors": [
    "Koenraad M. R. Audenaert"
  ],
  "comment": "14 pages; V2: minor typographic changes",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In previous work (see arxiv:1102.3040), we have defined the telescopic relative entropy (TRE), which is a regularisation of the quantum relative entropy $S(\\rho||\\sigma)=\\trace\\rho(\\log\\rho-\\log\\sigma)$, by replacing the second argument $\\sigma$ by a convex combination of the first and the second argument, $\\tau=a\\rho+(1-a)\\sigma$ and dividing the result by $-\\log a$. We also explored some basic properties of the TRE. In this follow-up paper we state and prove two upper bounds on the variation of the TRE when either the first or the second argument changes. These bounds are close in spirit to a triangle inequality. For the ordinary relative entropy no such bounds are possible due to the fact that the variation could be infinite.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-27T09:58:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangle inequality",
      "telescopic relative entropy-ii triangle inequalities",
      "second argument changes",
      "ordinary relative entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3041A"
    }
  }
}