{
  "annotation_id": "1dc2c493-e08d-49d4-944a-3370cb2b6f6c",
  "date_created": "2026-03-02T18:02:16.602000Z",
  "date_modified": "2026-03-02T18:02:16.602000Z",
  "file_hash": "e53b3e9b1b7f8be5298f9515fa86b04a353d89453f3324ae94398e81cff51e36",
  "private": false,
  "record": {
    "abstract": "In a partially observed quantum or classical system the information that we\ncannot access results in our description of the system becoming mixed even if\nwe have perfect initial knowledge. That is, if the system is quantum the\nconditional state will be given by a state matrix $\\rho_r(t)$ and if classical\nthe conditional state will be given by a probability distribution $P_r(x,t)$\nwhere $r$ is the result of the measurement. Thus to determine the evolution of\nthis conditional state under continuous-in-time monitoring requires an\nexpensive numerical calculation. In this paper we demonstrating a numerical\ntechnique based on linear measurement theory that allows us to determine the\nconditional state using only pure states. That is, our technique reduces the\nproblem size by a factor of $N$, the number of basis states for the system.\nFurthermore we show that our method can be applied to joint classical and\nquantum systems as arises in modeling realistic measurement.",
    "arxiv_id": "quant-ph/0503241",
    "authors": [
      "Jay Gambetta",
      "H. M. Wiseman"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1464-4266/7/10/008",
    "journal_ref": "Journal of Optics B: Quantum and Semiclassical Optics 7, S250\n  (2005)",
    "title": "Stochastic simulations of conditional states of partially observed   systems, quantum and classical",
    "url": "https://arxiv.org/abs/quant-ph/0503241"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3cbdd263-5831-44a0-938b-6dc7db4022f6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}