{
  "annotation_id": "d41a2a39-e89c-41cb-814f-8d47358691b8",
  "date_created": "2026-03-02T18:01:46.076000Z",
  "date_modified": "2026-03-02T18:01:46.076000Z",
  "file_hash": "c46c525dc2268f3989e47a252f2ee1809875b601a121c1f743d7c45f63adb285",
  "private": false,
  "record": {
    "abstract": "Suppose that the Hamiltonian acting on a quantum system is unknown and one\nwants to determine what is the Hamiltonian. We show that in general this\nrequires a time $\\Delta t$ which obeys the uncertainty relation $\\Delta t\n\\Delta H \\gtrsim 1$ where $\\Delta H$ is a measure of how accurately the unknown\nHamiltonian must be estimated. We then apply this result to the problem of\nmeasuring the energy of an unknown quantum state. It has been previously shown\nthat if the Hamiltonian is known, then the energy can in principle be measured\nin an arbitrarily short time. On the other hand we show that if the Hamiltonian\nis not known then an energy measurement necessarily takes a minimum time\n$\\Delta t$ which obeys the uncertainty relation $\\Delta t \\Delta E \\gtrsim 1$\nwhere $\\Delta E$ is the precision of the energy measurement. Several examples\nare studied to address the question of whether it is possible to saturate these\nuncertainty relations. Their interpretation is discussed in detail.",
    "arxiv_id": "quant-ph/0110004",
    "authors": [
      "Y. Aharonov",
      "S. Massar",
      "S. Popescu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.66.052107",
    "journal_ref": "Phys. Rev. A 66, 052107 (2002)",
    "title": "Measuring Energy, Estimating Hamiltonians, and the Time-Energy   Uncertainty Relation",
    "url": "https://arxiv.org/abs/quant-ph/0110004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c40e8a4d-5267-44b9-a748-0b0fe426c895",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}