{
  "id": "quant-ph/0412030",
  "version": "v1",
  "published": "2004-12-03T22:01:32.000Z",
  "updated": "2004-12-03T22:01:32.000Z",
  "title": "Generalized uncertainty relations and efficient measurements in quantum systems",
  "authors": [
    "V. P. Belavkin"
  ],
  "comment": "17 pages. Translated from Russian and typeset in LaTeX from Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, March, 1976",
  "journal": "Teoreticheskaya i Matematichescheskaya Fizika, Vol. 26, No.3 pp. 316--329, Plenum, 1976",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this inequality leads to a precise formulation of a generalized uncertainty principle for arbitrary states, in contrast to Helstrom's symmetric variant in which these relations are obtained only for pure states. A notion of canonical states is introduced and the lower mean square error bound is found for estimating of the parameters of canonical states, in particular, the canonical parameters of a Lie group. It is shown that these bounds are globally attainable only for canonical states for which there exist efficient measurements or quasimeasurements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-03T22:01:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized uncertainty relations",
      "efficient measurements",
      "quantum systems",
      "canonical states",
      "lower mean square error bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph.12030B"
    }
  }
}