{
  "annotation_id": "3d1e52a5-8ba3-4762-9661-a1907757c4fb",
  "date_created": "2026-03-02T18:01:58.861000Z",
  "date_modified": "2026-03-02T18:01:58.861000Z",
  "file_hash": "a54813e6fe531ecadf2a86db83310a293efa8c27b1aa36f94ca6447ba1f8165e",
  "private": false,
  "record": {
    "abstract": "We compute the volume of the N^2-1 dimensional set M_N of density matrices of\nsize N with respect to the Bures measure and show that it is equal to that of a\nN^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume\nof the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the\nboundary of the set M_N and obtain analogous results for the smaller set of all\nreal density matrices. An explicit formula for the Bures-Hall normalization\nconstants is derived for an arbitrary N.",
    "arxiv_id": "quant-ph/0304041",
    "authors": [
      "Hans-Juergen Sommers",
      "Karol Zyczkowski"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/39/308",
    "journal_ref": "J. Phys. A 36, 10083-10100 (2003)",
    "title": "Bures volume of the set of mixed quantum states",
    "url": "https://arxiv.org/abs/quant-ph/0304041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2d8213c4-ecb0-473b-97b1-e4c76b642df7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}