{
  "annotation_id": "a36c571e-905e-44e0-a4e1-4ab356f034cb",
  "date_created": "2026-03-02T18:02:45.026000Z",
  "date_modified": "2026-03-02T18:02:45.026000Z",
  "file_hash": "6629b45564757f523f6f0e426b5e0f45ba1f6f6575563ee92fa81acfd768d5ee",
  "private": false,
  "record": {
    "abstract": "The problem of of how many entangled or, respectively, separable states there\nare in the set of all quantum states is investigated. We study to what extent\nthe choice of a measure in the space of density matrices describing\nN--dimensional quantum systems affects the results obtained. We demonstrate\nthat the link between the purity of the mixed states and the probability of\nentanglement is not sensitive to the measure chosen. Since the criterion of\npartial transposition is not sufficient to distinguish all separable states for\nN \u003e 6, we develop an efficient algorithm to calculate numerically the\nentanglement of formation of a given mixed quantum state, which allows us to\ncompute the volume of separable states for N=8 and to estimate the volume of\nthe bound entangled states in this case.",
    "arxiv_id": "quant-ph/9902050",
    "authors": [
      "Karol Zyczkowski"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.60.3496",
    "journal_ref": "Phys.Rev. A60 (1999) 3496",
    "title": "On the volume of the set of mixed entangled states II",
    "url": "https://arxiv.org/abs/quant-ph/9902050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1cbc5aa6-6cd6-4c70-9062-24748af46613",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}