{
  "annotation_id": "70010c06-5b98-4cb5-8509-15fed443b4a0",
  "date_created": "2026-03-02T18:01:39.271000Z",
  "date_modified": "2026-03-02T18:01:39.271000Z",
  "file_hash": "e5057f338e52b0bdf38eb7e60020dd6bb4e63bd781188de44878e9421a66fd18",
  "private": false,
  "record": {
    "abstract": "We discuss the entanglement properties of bipartite states with Gaussian\nWigner functions. Separability and the positivity of the partial transpose are\ncharacterized in terms of the covariance matrix of the state, and it is shown\nthat for systems composed of a single oscillator for Alice and an arbitrary\nnumber for Bob, positivity of the partial transpose implies separability.\nHowever, this implications fails with two oscillators on each side, as we show\nby a five parameter family of explicit counterexamples.",
    "arxiv_id": "quant-ph/0009118",
    "authors": [
      "R. F. Werner",
      "M. M. Wolf"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.86.3658",
    "title": "Bound entangled Gaussian states",
    "url": "https://arxiv.org/abs/quant-ph/0009118"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c2b0963c-336e-4795-b787-f96b44c8b832",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}