{
  "id": "1210.5048",
  "version": "v2",
  "published": "2012-10-18T08:07:03.000Z",
  "updated": "2013-06-22T13:20:59.000Z",
  "title": "Convergence of SDP hierarchies for polynomial optimization on the hypersphere",
  "authors": [
    "Andrew C. Doherty",
    "Stephanie Wehner"
  ],
  "comment": "45 pages, amsmath, comments welcome, for readers in quantum information: contains de Finetti theorem, v2: improved explanations, additional bound",
  "categories": [
    "math.OC",
    "cs.DS",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We show how to bound the accuracy of a family of semi-definite programming relaxations for the problem of polynomial optimization on the hypersphere. Our method is inspired by a set of results from quantum information known as quantum de Finetti theorems. In particular, we prove a de Finetti theorem for a special class of real symmetric matrices to establish the existence of approximate representing measures for moment matrix relaxations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-22T13:20:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial optimization",
      "sdp hierarchies",
      "hypersphere",
      "convergence",
      "finetti theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5048D"
    }
  }
}