{
  "annotation_id": "45a680e6-5fcf-4898-91cf-9baf989eb8c5",
  "date_created": "2026-03-02T18:02:13.278000Z",
  "date_modified": "2026-03-02T18:02:13.278000Z",
  "file_hash": "1d5524f4dfb581c1b103f33ac293503af29d90ddd5572fcfb6c357762300f4de",
  "private": false,
  "record": {
    "abstract": "Uncertainty relations for mixed quantum states (precisely, purity-bounded\nposition-momentum relations, developed by Bastiaans and then by Man\u0027ko and\nDodonov) are studied in general multi-dimensional case. An expression for\nfamily of mixed states at the lower bound of uncertainty relation is obtained.\nIt is shown, that in case of entropy-bounded uncertainty relations, lower-bound\nstate is thermal, and a transition from one-dimensional problem to\nmulti-dimensional one is trivial. Results of numerical calculation of the\nrelation lower bound for different types of generalized purity are presented.\nAnalytical expressions for general purity-bounded relations for highly mixed\nstates are obtained.",
    "arxiv_id": "quant-ph/0411067",
    "authors": [
      "Mikalai Karelin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/28/012",
    "journal_ref": "J. Phys. A: Math. Gen., vol. 38, pp. 6393-6403 (2005)",
    "title": "Purity-bounded uncertainty relations in multidimensional space --   generalized purity",
    "url": "https://arxiv.org/abs/quant-ph/0411067"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3dde9cb3-7214-48be-bae3-9239f1b8fb4e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}