{
  "annotation_id": "6f58d6c4-1bf9-4462-be0c-7a6fc6222f95",
  "date_created": "2026-03-02T18:02:29.889000Z",
  "date_modified": "2026-03-02T18:02:29.889000Z",
  "file_hash": "84e6789011948df8c1cf1294a932d7353f909cdd6c261918e576cbc458962137",
  "private": false,
  "record": {
    "abstract": "We study the separability of bipartite quantum systems in arbitrary\ndimensions using the Bloch representation of their density matrix. This\napproach enables us to find an alternative characterization of the separability\nproblem, from which we derive a necessary condition and sufficient conditions\nfor separability. For a certain class of states the necessary condition and a\nsufficient condition turn out to be equivalent, therefore yielding a necessary\nand sufficient condition. The proofs of the sufficient conditions are\nconstructive, thus providing decompositions in pure product states for the\nstates that satisfy them. We provide examples that show the ability of these\nconditions to detect entanglement. In particular, the necessary condition is\nproved to be strong enough to detect bound entangled states.",
    "arxiv_id": "quant-ph/0607195",
    "authors": [
      "Julio I. de Vicente"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.26421/QIC7.7-5",
    "journal_ref": "Quantum Inf. Comput. 7, 624 (2007)",
    "title": "Separability criteria based on the Bloch representation of density   matrices",
    "url": "https://arxiv.org/abs/quant-ph/0607195"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3662b51f-aeec-446c-97d8-f5e2b7848e75",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}