{
  "annotation_id": "56c3a6d8-0441-408c-8932-05f43fe0d23a",
  "date_created": "2026-03-02T18:02:27.660000Z",
  "date_modified": "2026-03-02T18:02:27.660000Z",
  "file_hash": "888abb5ac0d2020a266266e56d6da090a9fb864127bc6983973ea313ec84082c",
  "private": false,
  "record": {
    "abstract": "Necessary and sufficient observable conditions for the nonnegativity of all\npartial transpositions of multi-mode quantum states are derived. The result is\na hierarchy of inequalities for minors in terms of moments of the given state.\nViolations of any inequality is a sufficient condition for entanglement. Full\nentanglement can be certified for a manifold of multi-mode quantum states. A\n\\textit{Mathematica} package is given for a systematic test of the hierarchy of\nconditions.",
    "arxiv_id": "quant-ph/0605154",
    "authors": [
      "E. Shchukin",
      "W. Vogel"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.030302",
    "title": "Multipartite continuous-variable entanglement",
    "url": "https://arxiv.org/abs/quant-ph/0605154"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d2e92c35-2f07-499b-861d-54da2a2cf021",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}