{
  "id": "1306.0349",
  "version": "v2",
  "published": "2013-06-03T11:00:15.000Z",
  "updated": "2013-09-02T14:17:13.000Z",
  "title": "Decomposition of any quantum measurement into extremals",
  "authors": [
    "G. Sentís",
    "B. Gendra",
    "S. D. Bartlett",
    "A. C. Doherty"
  ],
  "comment": "10 pages",
  "journal": "J. Phys. A: Math. Theor. 46 (2013) 375302",
  "doi": "10.1088/1751-8113/46/37/375302",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1 POVMs are needed. For a measurement with $N$ elements on a $d$-dimensional space, our algorithm will decompose it into at most $(N-1)d+1$ extremals, whereas the best previously known upper bound scaled as $d^2$. Since the decomposition is not unique, we show how to tailor our algorithm to provide particular types of decompositions that exhibit some desired property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-02T14:17:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decomposition",
      "upper bound",
      "extremal measurements",
      "generalized quantum measurement",
      "dimensional space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Sep",
      "volume": 46,
      "number": 37,
      "pages": 375302
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhA...46K5302S"
    }
  }
}