{
  "annotation_id": "130fe03e-4d42-4f71-932e-f12444da98a1",
  "date_created": "2026-03-02T18:02:34.697000Z",
  "date_modified": "2026-03-02T18:02:34.697000Z",
  "file_hash": "3cfac178194fa55ed9cdbbfdb40cdaf3e2a029db182c7b6c4bc5cda27f9f3acc",
  "private": false,
  "record": {
    "abstract": "The separability problem is formulated in terms of a characterization of a\nsingle entanglement witness. More specifically, we show that any (in general\nmultipartite) state \\varrho is separable if and only if a specially constructed\nentanglement witness W_{\\varrho} is weakly optimal, i.e., its expectation value\nvanishes on at least one product vector. Interestingly, the witness can always\nbe chosen to be decomposable. Our result changes the conceptual aspect of the\nseparability problem and rises some questions about properties of positive\nmaps.",
    "arxiv_id": "quant-ph/0703097",
    "authors": [
      "Piotr Badzi\u0105g",
      "Pawe\u0142 Horodecki",
      "Ryszard Horodecki",
      "Remigiusz Augusiak"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.88.010301",
    "journal_ref": "Physical Review A 88, 010301(R) (2013)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Separability in terms of a single entanglement witness",
    "url": "https://arxiv.org/abs/quant-ph/0703097"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "368d6197-15c6-4984-b5c3-595bd959254b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}