{
  "annotation_id": "a51006ac-ac3d-46db-ab3b-38e389d215ad",
  "date_created": "2026-03-02T18:01:56.063000Z",
  "date_modified": "2026-03-02T18:01:56.063000Z",
  "file_hash": "1a7817eb50a3e2b2ab5f003055be877559df9e114dac29005fd68d1bfaf7f7a1",
  "private": false,
  "record": {
    "abstract": "We compute the volume of the convex N^2-1 dimensional set M_N of density\nmatrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area\nof the boundary of this set is also found and its ratio to the volume provides\nan information about the complex structure of M_N. Similar investigations are\nalso performed for the smaller set of all real density matrices. As an\nintermediate step we analyze volumes of the unitary and orthogonal groups and\nof the flag manifolds.",
    "arxiv_id": "quant-ph/0302197",
    "authors": [
      "Karol Zyczkowski",
      "Hans-Juergen Sommers"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/36/39/310",
    "journal_ref": "J. Phys. A 36, 10115-10130 (2003)",
    "title": "Hilbert--Schmidt volume of the set of mixed quantum states",
    "url": "https://arxiv.org/abs/quant-ph/0302197"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a453eddb-e22b-4342-bcd1-f6146d3e520a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}