{
  "annotation_id": "8276cf2c-0462-47f4-a37b-55a5f9d189e2",
  "date_created": "2026-03-02T18:02:23.773000Z",
  "date_modified": "2026-03-02T18:02:23.773000Z",
  "file_hash": "522c7f345a8b851404b96e0d1d5f94012f1a6d7a764f4b06ffa8ba03767a9066",
  "private": false,
  "record": {
    "abstract": "Measurements continuous in time were consistently introduced in quantum\nmechanics and applications worked out, mainly in quantum optics. In this\ncontext a quantum filtering theory has been developed giving the reduced state\nafter the measurement when a certain trajectory of the measured observables is\nregistered (the a posteriori states). In this paper a new derivation of\nfiltering equations is presented, in the cases of counting processes and of\nmeasurement processes of diffusive type. It is also shown that the equation for\nthe a posteriori dynamics in the diffusive case can be obtained, by a suitable\nlimit, from that one in the counting case. Moreover, the paper is intended to\nclarify the meaning of the various concepts involved and to discuss the\nconnections among them. As an illustration of the theory, simple models are\nworked out.",
    "arxiv_id": "quant-ph/0512189",
    "authors": [
      "A. Barchielli",
      "V. P. Belavkin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/24/7/022",
    "journal_ref": "J. Phys. A: Math. Gen. 24 (1991) 1495--1514",
    "title": "Measurements continuous in time and a posteriori states in quantum",
    "url": "https://arxiv.org/abs/quant-ph/0512189"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "423415ed-9ce2-49c8-9935-4b0cd7a73fa6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}