{
  "annotation_id": "df0d0aa4-7929-40a6-9e95-00f397907443",
  "date_created": "2026-03-02T18:01:59.934000Z",
  "date_modified": "2026-03-02T18:01:59.934000Z",
  "file_hash": "33a25dbe01544f03b03379b06e07bb4206cddf3df04edd1f4d038848375cff23",
  "private": false,
  "record": {
    "abstract": "Lueders theorem states that two observables commute if measuring one of them\ndoes not disturb the measurement outcomes of the other. We study measurements\nwhich are described by continuous positive operator-valued measurements (or\nPOVMs) associated with coherent states on a Lie group. In general, operators\nturn out to be invariant under the Lueders map if their P- and Q-symbols\ncoincide. For a spin corresponding to SU(2), the identity is shown to be the\nonly operator with this property. For a particle, a countable family of\nlinearly independent operators is identified which are invariant under the\nLueders map generated by the coherent states of the Heisenberg-Weyl group, H_3.\nThe Lueders map is also shown to implement the anti-normal ordering of creation\nand annihilation operators of a particle.",
    "arxiv_id": "quant-ph/0308035",
    "authors": [
      "Stefan Weigert",
      "Paul Busch"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1623001",
    "journal_ref": "J. Math. Phys. 44 (2003) 5474",
    "title": "Lueders Theorem for Coherent-State POVMs",
    "url": "https://arxiv.org/abs/quant-ph/0308035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1bf7ef10-ba4d-4bef-8028-c3619444caf9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}