{
  "annotation_id": "82c037ff-dbeb-4041-a2f7-6b9995ba0e93",
  "date_created": "2026-03-02T18:02:20.657000Z",
  "date_modified": "2026-03-02T18:02:20.657000Z",
  "file_hash": "a756d2c1930984ea236215798d3808d57a9a93e9c62f48eeccd336e45052bc11",
  "private": false,
  "record": {
    "abstract": "A hierarchy of multimode uncertainty relations on the second moments of n\npairs of canonical operators is derived in terms of quantities invariant under\nlinear canonical (i.e. symplectic) transformations. Conditions for the\nseparability of multimode continuous variable states are derived from the\nuncertainty relations, generalizing the inequalities obtained in [Phys. Rev.\nLett. 96, 110402 (2006)] to states with some transposed symplectic eigenvalues\nequal to 1. Finally, to illustrate the methodology proposed for the detection\nof continuous variable entanglement, the separability of multimode noisy\nGHZ-like states is analysed in detail with the presented techniques, deriving a\nnecessary and sufficient condition for the separability of such states under an\n`even\u0027 bipartition of the modes.",
    "arxiv_id": "quant-ph/0508231",
    "authors": [
      "Alessio Serafini"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevLett.96.110402",
    "journal_ref": "J. Opt. Soc. Am. B 24, 347-354 (2007)",
    "title": "Detecting multimode entanglement by symplectic uncertainty relations",
    "url": "https://arxiv.org/abs/quant-ph/0508231"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f879ee0e-5802-40ec-a336-76acc120c5bd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}