{
  "annotation_id": "28e4e669-d669-4200-9729-1d19223dfe08",
  "date_created": "2026-03-02T18:02:23.767000Z",
  "date_modified": "2026-03-02T18:02:23.767000Z",
  "file_hash": "7c45175a4d00d7b51a79a9d3b12795de9a3b85f1d06d1422d274324b4524d172",
  "private": false,
  "record": {
    "abstract": "Based on the ranks of reduced density matrices, we derive necessary\nconditions for the separability of multiparticle arbitrary-dimensional mixed\nstates, which are equivalent to sufficient conditions for entanglement. In a\nsimilar way we obtain necessary conditions for the separability of a given\nmixed state with respect to partitions of all particles of the system into\nsubsets. The special case of pure states is discussed separately.",
    "arxiv_id": "quant-ph/0512199",
    "authors": [
      "Bo Chong",
      "Hellmut Keiter",
      "Joachim Stolze"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Multiparticle entanglement and ranks of density matrices",
    "url": "https://arxiv.org/abs/quant-ph/0512199"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "036c88aa-76da-4d36-95ca-3d423aa94bb4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}