{
  "annotation_id": "722d252f-7c2f-4125-ac84-d30a9b97a2f0",
  "date_created": "2026-03-02T18:02:41.659000Z",
  "date_modified": "2026-03-02T18:02:41.659000Z",
  "file_hash": "c6930f87e55697c53d185c3b8f2ffac39cb3729bc023b3b8f9a30b7c41b38c22",
  "private": false,
  "record": {
    "abstract": "A natural measure in the space of density matrices describing N-dimensional\nquantum systems is proposed. We study the probability P that a quantum state\nchosen randomly with respect to the natural measure is not entangled (is\nseparable). We find analytical lower and upper bounds for this quantity.\nNumerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate\nthat P decreases exponentially with N. Analysis of a conditional measure of\nseparability under the condition of fixed purity shows a clear dualism between\npurity and separability: entanglement is typical for pure states, while\nseparability is connected with quantum mixtures. In particular, states of\nsufficiently low purity are necessarily separable.",
    "arxiv_id": "quant-ph/9804024",
    "authors": [
      "Karol Zyczkowski",
      "Pawel Horodecki",
      "Anna Sanpera",
      "Maciej Lewenstein"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.58.883",
    "journal_ref": "Phys.Rev. A58 (1998) 883",
    "title": "On the volume of the set of mixed entangled states",
    "url": "https://arxiv.org/abs/quant-ph/9804024"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "66e887de-b937-4106-9fc0-f02c79035882",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}