{
  "annotation_id": "389e692a-d6de-4d02-a49f-15b1c4dbb0a4",
  "date_created": "2026-03-02T18:02:36.801000Z",
  "date_modified": "2026-03-02T18:02:36.801000Z",
  "file_hash": "8f112042b86d82ec39025f7ca650aceaa016f2969a4b893e4a91c680d35a03be",
  "private": false,
  "record": {
    "abstract": "Calling the quantity; 2delta(A)delta(B)/|\u003c[A, B]\u003e|, with non-zero\ndenominator, the uncertainty product ratio or UPR for the pair of observables,\n(A, B), it is shown that any non-zero correlation coefficient between two\nobservables raises, above unity, the lower bound of the UPR for each member of\nan infinite collection of pairs of incompatible observables. Conversely, any\nUPR is subject to lower bounds above unity determined by each of an infinite\ncollection of correlation coefficients. This result generalizes the well known\nSchroedinger strengthening of the Robertson uncertainty relations (with the\nformer expressed in terms of the correlation coefficient rather than the\nanticommutator) where the UPR and the correlation coefficient both involve the\nsame pair of observables. Two, independent, derivations of the result are\npresented to clarify its origins and some examples of its use are examined.",
    "arxiv_id": "quant-ph/0703226",
    "authors": [
      "Gordon N. Fleming"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Correlation coefficients and the Robertson-Schroedinger uncertainty   relations",
    "url": "https://arxiv.org/abs/quant-ph/0703226"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8acacaf3-ed93-4f2c-a7a3-1da84f5593be",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}