{
  "annotation_id": "c1b188e7-d383-43d2-af4e-28a8aad9169a",
  "date_created": "2026-03-02T18:01:39.347000Z",
  "date_modified": "2026-03-02T18:01:39.347000Z",
  "file_hash": "6251227172b13b4f5348022b3b7d642ef9ed1fb4bdd5c107acd637d57c16d715",
  "private": false,
  "record": {
    "abstract": "We provide necessary and sufficient conditions for separability of mixed\nstates of n-particle systems. The conditions are formulated in terms of maps\nwhich are positive on product states of $n-1$ particles. The method of\nproviding of the maps on the basis of unextendable product bases is provided.\nThe three qubit state problem is reformulated in the form suggesting\npossibility of explicite characterisation of all maps needed for separability\ncondition.",
    "arxiv_id": "quant-ph/0006071",
    "authors": [
      "Michal Horodecki",
      "Pawel Horodecki",
      "Ryszard Horodecki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(01)00142-6",
    "title": "Separability of n-particle mixed states: necessary and sufficient   conditions in terms of linear maps",
    "url": "https://arxiv.org/abs/quant-ph/0006071"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b51eeef0-bf0c-4737-8d17-d650de301ab7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}