{
  "annotation_id": "69ffcda5-1380-4c82-84e5-85601e5fdcd7",
  "date_created": "2026-03-02T18:02:41.153000Z",
  "date_modified": "2026-03-02T18:02:41.153000Z",
  "file_hash": "05bf29e6c5f7e71cbb8954203a839dcd45fa3f08753e4a1bdde3d5ea15139fc3",
  "private": false,
  "record": {
    "abstract": "To find the Hermitian phase operatorof a single-mode electromagnetic field in\nquantum mechanics, the Schroedinger representation is extended to a larger\nHilbert space augmented by states with infinite excitation by nonstandard\nanalysis. The Hermitian phase operator is shown to exist on the extended\nHilbert space. This operator is naturally considered as the controversial limit\nof the approximate phase operators on finite dimensional spaces proposed by\nPegg and Barnett. The spectral measure of this operator is a Naimark extension\nof the optimal probability operator-valued measure for the phase parameter\nfound by Helstrom. Eventually, the two promising approaches to the statistics\nof the phase in quantum mechanics is unified by means of the Hermitian phase\noperator in the macroscopic extension of the Schroedinger representation.",
    "arxiv_id": "quant-ph/9705034",
    "authors": [
      "Masanao Ozawa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1006/aphy.1997.5685",
    "journal_ref": "Annals Phys. 257 (1997) 65",
    "title": "Phase Operator Problem and Macroscopic Extension of Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9705034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4546c48f-b2a9-4559-bbb3-b934e5598622",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}