{
  "id": "quant-ph/0506267",
  "version": "v2",
  "published": "2005-06-30T13:31:40.000Z",
  "updated": "2005-08-26T14:15:52.000Z",
  "title": "Optimal estimation of group transformations using entanglement",
  "authors": [
    "G. Chiribella",
    "G. M. D'Ariano",
    "M. F. Sacchi"
  ],
  "comment": "11 pages, no figures",
  "journal": "Phys. Rev. A 72 042338 (2005)",
  "doi": "10.1103/PhysRevA.72.042338",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We derive the optimal input states and the optimal quantum measurements for estimating the unitary action of a given symmetry group, showing how the optimal performance is obtained with a suitable use of entanglement. Optimality is defined in a Bayesian sense, as minimization of the average value of a given cost function. We introduce a class of cost functions that generalizes the Holevo class for phase estimation, and show that for states of the optimal form all functions in such a class lead to the same optimal measurement. A first application of the main result is the complete proof of the optimal efficiency in the transmission of a Cartesian reference frame. As a second application, we derive the optimal estimation of a completely unknown two-qubit maximally entangled state, provided that N copies of the state are available. In the limit of large N, the fidelity of the optimal estimation is shown to be 1-3/(4N).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-08-26T14:15:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal estimation",
      "group transformations",
      "entanglement",
      "cost function",
      "cartesian reference frame"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}