{
  "annotation_id": "dcbaf3a4-74ca-49c0-b183-1b01a5cbec7d",
  "date_created": "2026-03-02T18:01:59.397000Z",
  "date_modified": "2026-03-02T18:01:59.397000Z",
  "file_hash": "13cababa49447a9ab7608fcdea76c017619d3808febebf2abfe4743b7313560e",
  "private": false,
  "record": {
    "abstract": "In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently\nproposed uncertainty relations for a quantum particle on a circle. He states\nthat (i) the quantity $\\Delta^2(\\hat\\phi)$ introduced by us representing the\nuncertainty of the angle is not a proper measure of the position uncertainty\nand therefore the proposed inequalities can hardly be qualified as a relevant\nuncertainty relations on a circle; and that (ii) the most suitable uncertainty\nrelations on a circle are those based on the Gram-Robertson matrix. It is shown\nby examples that both points are erroneous.",
    "arxiv_id": "quant-ph/0305069",
    "authors": [
      "K. Kowalski",
      "J. Rembielinski"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/20/323",
    "journal_ref": "J. Phys. A: Math. Gen. 36 (2003) 5695-5698",
    "title": "Reply to the Comment on ``On the uncertainty relations and squeezed   states for the quantum mechanics on a circle\u0027\u0027",
    "url": "https://arxiv.org/abs/quant-ph/0305069"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0d0134b5-6486-49b5-9bdf-690609465890",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}