{
  "annotation_id": "64c2c0e1-33ae-4395-a48a-00498c6dc22f",
  "date_created": "2026-03-02T18:01:59.926000Z",
  "date_modified": "2026-03-02T18:01:59.926000Z",
  "file_hash": "171ed53c27b9e4b8262a99f2ffa085d4c1356a2100fd0b35e4c72dde699469e8",
  "private": false,
  "record": {
    "abstract": "Phase-locking governs the phase noise in classical clocks through effects\ndescribed in precise mathematical terms. We seek here a quantum counterpart of\nthese effects by working in a finite Hilbert space. We use a coprimality\ncondition to define phase-locked quantum states and the corresponding\nPegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are\nrevealed and related to Ramanujan sums in the theory of prime numbers. The\nemployed mathematical procedures also emphasize the isomorphism between\nalgebraic number theory and the theory of quantum entanglement",
    "arxiv_id": "quant-ph/0304101",
    "authors": [
      "M. Planat",
      "H. C. Rosu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(03)00942-3",
    "journal_ref": "Phys. Lett. A 315 (2003) 1-5",
    "title": "Cyclotomy and Ramanujan sums in quantum phase locking",
    "url": "https://arxiv.org/abs/quant-ph/0304101"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2b58ce76-8980-4af9-9e16-2355e737eeb7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}