{
  "id": "math-ph/0505085",
  "version": "v2",
  "published": "2005-05-31T13:34:30.000Z",
  "updated": "2005-06-02T12:46:27.000Z",
  "title": "A Note on the p->q norms of Completely Positive Maps",
  "authors": [
    "Koenraad M. R. Audenaert"
  ],
  "comment": "1.5 pages; a different proof of the main statement has already appeared in: J. Watrous, QIC 5, 58-68 (2005)",
  "journal": "Lin. Alg. Appl 430(4), 1436-1440 (2009)",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "King and Ruskai asked whether the $p\\to q$ norm of a completely positive map $\\Phi$, acting between Schatten $p$ and $q$ classes of self-adjoint operators, $||\\Phi||_{p\\to q} = \\max_{A=A^*} \\frac{||\\Phi(A)||_q}{||A||_p}$, is equal to the $p\\to q$ norm of that map when acting between Schatten classes of general, not necessarily self-adjoint, operators. The first proof has been given by Watrous. We give an alternative proof of this statement.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-02T12:46:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive map",
      "self-adjoint operators",
      "first proof",
      "schatten classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph...5085A"
    }
  }
}