{
  "annotation_id": "7012f19d-ae67-4122-aa6d-99d51f181a05",
  "date_created": "2026-03-02T18:01:42.648000Z",
  "date_modified": "2026-03-02T18:01:42.648000Z",
  "file_hash": "82576220169cb10fbfd2f7be8d7daef8cb5fe6c896e3f46e06b6eff5b5b842c6",
  "private": false,
  "record": {
    "abstract": "We derive differential equations for the modified Feynman propagator and for\nthe density operator describing time-dependent measurements or histories\ncontinuous in time. We obtain an exact series solution and discuss its\napplications. Suppose the system is initially in a state with density operator\n$\\rho(0)$ and the projection operator $E(t) = U(t) E U^\\dagger(t)$ is measured\ncontinuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\\rho(0) E\n= \\rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness\nconditions in $t$. Then the probability of always finding $E(t) = 1$ from $t =\n0$ to $T$ is unity. Generically $E(T) \\neq E$ and the watched system is sure to\nchange its state, which is the anti-Zeno paradox noted by us recently. Our\nresults valid for projectors of arbitrary rank generalize those obtained by\nAnandan and Aharonov for projectors of unit rank.",
    "arxiv_id": "quant-ph/0102019",
    "authors": [
      "A. P. Balachandran",
      "S. M. Roy"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th"
    ],
    "doi": "10.1142/S0217751X0201056X",
    "journal_ref": "Int.J.Mod.Phys.A17:4007-4024,2002",
    "title": "Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with   Applications",
    "url": "https://arxiv.org/abs/quant-ph/0102019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "633bf057-f4fa-4714-b7b1-61051f62e2ac",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}