{
  "annotation_id": "535f73a5-473f-42c5-9775-4ac65c7a8743",
  "date_created": "2026-03-02T18:02:06.638000Z",
  "date_modified": "2026-03-02T18:02:06.638000Z",
  "file_hash": "708c755394cfe11b940ab2bc792f2135d0c5b094afb30d6b5ee47461dfefddba",
  "private": false,
  "record": {
    "abstract": "We prove an uncertainty relation, which imposes a bound on any joint\nmeasurement of position and momentum. It is of the form $(\\Delta P)(\\Delta\nQ)\\geq C\\hbar$, where the `uncertainties\u0027 quantify the difference between the\nmarginals of the joint measurement and the corresponding ideal observable.\nApplied to an approximate position measurement followed by a momentum\nmeasurement, the uncertainties become the precision $\\Delta Q$ of the position\nmeasurement, and the perturbation $\\Delta P$ of the conjugate variable\nintroduced by such a measurement.\n  We also determine the best constant $C$, which is attained for a unique phase\nspace covariant measurement.",
    "arxiv_id": "quant-ph/0405184",
    "authors": [
      "R. F. Werner"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The uncertainty relation for joint measurement of position and momentum",
    "url": "https://arxiv.org/abs/quant-ph/0405184"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "472ebfd7-0753-4b02-885a-f0cc8c3b05a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}