{
  "annotation_id": "260d54af-b3ea-4fd5-8c02-067316cb82f2",
  "date_created": "2026-03-02T18:02:27.470000Z",
  "date_modified": "2026-03-02T18:02:27.470000Z",
  "file_hash": "aade610842bea99e1551f0a7f545a4b8d000bf0172aad8f4c52866cb949f983a",
  "private": false,
  "record": {
    "abstract": "Inseparability criteria for continuous and discrete bipartite quantum states\nbased on moments of annihilation and creation operators are studied by\ndeveloping the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. {\\bf 95},\n230502 (2005)]. If a state is separable, then the corresponding matrix of\nmoments is separable too. Thus, we derive generalized criteria, based on the\nseparability properties of the matrix of moments, are thus derived. In\nparticular, a new criterion based on realignment of moments in the matrix is\nproposed as an analogue of the standard realignment criterion for density\nmatrices. Other inseparability inequalities are obtained by applying positive\nmaps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to\ndescribe bipartite-entanglement of more than two modes is demonstrated: We\nobtain some previously known three-mode inseparability criteria originally\nderived from the Cauchy-Schwarz inequality, and we introduce new ones.",
    "arxiv_id": "quant-ph/0605001",
    "authors": [
      "A. Miranowicz",
      "M. Piani",
      "P. Horodecki",
      "R. Horodecki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.80.052303",
    "journal_ref": "Phys. Rev. A 80, 052303 (2009).",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Inseparability criteria based on matrices of moments",
    "url": "https://arxiv.org/abs/quant-ph/0605001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "32db8bd4-f518-43d0-8428-d223c73c9146",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}