{
  "annotation_id": "fffd6315-cd93-481e-a615-3d19d99dc352",
  "date_created": "2026-03-02T18:02:31.153000Z",
  "date_modified": "2026-03-02T18:02:31.153000Z",
  "file_hash": "bbb0f15bfcbc3e0b181796a929f7da75f41cb86f4d8e12428e8c5a64b84d266e",
  "private": false,
  "record": {
    "abstract": "Quantum mechanical uncertainty relations for position and momentum are\nexpressed in the form of inequalities involving the Renyi entropies. The proof\nof these inequalities requires the use of the exact expression for the\n(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.\nAnalogous uncertainty relations are derived for angle and angular momentum and\nalso for a pair of complementary observables in N-level systems. All these\nuncertainty relations become more attractive when expressed in terms of the\nsymmetrized Renyi entropies.",
    "arxiv_id": "quant-ph/0608116",
    "authors": [
      "Iwo Bialynicki-Birula"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.052101",
    "journal_ref": "Phys. Rev. A 74, 052101 (2006)",
    "title": "Formulation of the uncertainty relations in terms of the Renyi entropies",
    "url": "https://arxiv.org/abs/quant-ph/0608116"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "02e44f83-9d9d-4622-8175-3a2e76c1f7e9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}