{
  "annotation_id": "4ec73274-e167-4e6e-94fb-5a0ce9d8d1ed",
  "date_created": "2026-03-02T18:02:48.541000Z",
  "date_modified": "2026-03-02T18:02:48.541000Z",
  "file_hash": "f881e5477d6451272ea61921a67f690d385705c16e0eab748dec874c84652721",
  "private": false,
  "record": {
    "abstract": "We study the correspondence between classical and quantum measurements on a\nharmonic oscillator that describes a one-mode bosonic field. We connect the\nquantum measurement of an observable of the field with the possibility of\namplifying the observable ideally through a quantum amplifier. The\n``classical\u0027\u0027 measurement corresponds to the joint measurement of the position\n$q$ and momentum $p$ of the harmonic oscillator, with following evaluation of a\nfunction $f$ of the outcome $\\alpha=q+ip$. For the electromagnetic field the\njoint measurement is achieved by a heterodyne detector. The quantum measurement\nof an observable $\\hat O$ is obtained by preamplifying the heterodyne detector\nthrough an ideal amplifier of $\\hat O$, and rescaling the outcome by the gain\n$g$. We give a general criterion which states when this preamplified heterodyne\ndetection scheme approaches the ideal quantum measurement of $\\hat O$ in the\nlimit of infinite gain. We show that this criterion is satisfied and the ideal\nmeasurement is achieved for the case of the photon number operator and for the\nquadrature. For both operators the method is robust to nonunit quantum\nefficiency of the heterodyne detector. On the other hand, we show that the\npreamplified heterodyne detection scheme does not work for arbitrary observable\nof the field. As a counterexample, we prove that the simple quadratic function\nof the field $\\hat K=i(a^{\\dag 2}-a^2)/2$ has no corresponding polynomial\nfunction $f(\\alpha,\\bar \\alpha)$---including the obvious choice\n$f=\\hbox{Im}(\\alpha^2)$---that allows the measurement of $\\hat K$ through the\npreamplified heterodyne measurement scheme.",
    "arxiv_id": "quant-ph/9907057",
    "authors": [
      "G. M. D\u0027Ariano",
      "M. F. Sacchi",
      "H. P. Yuen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217979299002861",
    "journal_ref": "Int.J.Mod.Phys. B13 (1999) 3069-3086",
    "title": "On the correspondence between classical and quantum measurements on a   bosonic field",
    "url": "https://arxiv.org/abs/quant-ph/9907057"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9ddc8f7-1efc-45ea-afd6-08b454946ff3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}