{
  "annotation_id": "080a7eff-1bef-49f9-a1a3-81c33928caee",
  "date_created": "2026-03-02T18:02:13.686000Z",
  "date_modified": "2026-03-02T18:02:13.686000Z",
  "file_hash": "903ed5817cc8aad8178a26127111d0a16f53cc88131a215258955a8bc2890006",
  "private": false,
  "record": {
    "abstract": "Entropic uncertainty relations, based on sums of entropies of probability\ndistributions arising from different measurements on a given pure state, can be\nseen as a generalization of the Heisenberg uncertainty relation that is in many\ncases a more useful way to quantify incompatibility between observables. Of\nparticular interest are relationships between `mutually unbiased\u0027 observables,\nwhich are maximally incompatible. Lower bounds on the sum of entropies for sets\nof two such observables, and for complete sets of observables within a space of\ngiven dimension, have been found. This paper explores relations in the\nintermediate regime of large, but far from complete, sets of unbiased\nobservables.",
    "arxiv_id": "quant-ph/0412083",
    "authors": [
      "Adam Azarchs"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Entropic uncertainty relations for incomplete sets of mutually unbiased   observables",
    "url": "https://arxiv.org/abs/quant-ph/0412083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ef7dbada-18d5-46a9-bbf3-bf2239f16e61",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}