{
  "annotation_id": "c80a98a9-cd89-4f92-b573-723c265c461d",
  "date_created": "2026-03-02T18:01:42.004000Z",
  "date_modified": "2026-03-02T18:01:42.004000Z",
  "file_hash": "f782940b80a854a26f264947f3ba7df482c58a956b3709a5e7dc7078ed11f2c4",
  "private": false,
  "record": {
    "abstract": "We analyze several product measures in the space of mixed quantum states. In\nparticular we study measures induced by the operation of partial tracing. The\nnatural, rotationally invariant measure on the set of all pure states of a N x\nK composite system, induces a unique measure in the space of N x N mixed states\n(or in the space of K x K mixed states, if the reduction takes place with\nrespect to the first subsystem). For K=N the induced measure is equal to the\nHilbert-Schmidt measure, which is shown to coincide with the measure induced by\nsingular values of non-Hermitian random Gaussian matrices pertaining to the\nGinibre ensemble. We compute several averages with respect to this measure and\nshow that the mean entanglement of $N \\times N$ pure states behaves as lnN-1/2.",
    "arxiv_id": "quant-ph/0012101",
    "authors": [
      "Karol Zyczkowski",
      "Hans-Juergen Sommers"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/34/35/335",
    "journal_ref": "J. Phys. A34, 7111-7125 (2001)",
    "title": "Induced measures in the space of mixed quantum states",
    "url": "https://arxiv.org/abs/quant-ph/0012101"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6ff7de70-9626-430c-8104-35c2309a10c8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}