{
  "annotation_id": "20e9fb83-2d15-42d9-bff8-016e0f299324",
  "date_created": "2026-03-02T18:02:17.250000Z",
  "date_modified": "2026-03-02T18:02:17.250000Z",
  "file_hash": "e5fb42cd7d2414de5bd4af9b0dab411320c2989cff458a6fb1aa79b5cfd120b1",
  "private": false,
  "record": {
    "abstract": "The reduction criterion is a well known necessary condition for separable\nstates, and states violating this condition are entangled and also\n1-distillable. In this paper we introduce a new set of necessary conditions for\nseparability of multipartite states, obtained from a set of positive but not\ncompletely positive maps. These conditions can be thought of as generalisations\nof the reduction criterion to multipartite systems. We use tripartite Werner\nstates as an example to investigate the entanglement detecting powers of some\nof these new conditions, and we also look at what these conditions mean in\nterms of distillation. Finally, we show that these maps can be used to give a\npartial solution to the subsystem problem, as described in Ref. [14].",
    "arxiv_id": "quant-ph/0504154",
    "authors": [
      "William Hall"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.72.022311",
    "title": "Multipartite reduction criteria for separability",
    "url": "https://arxiv.org/abs/quant-ph/0504154"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bde2604b-3926-4cde-a8f7-5d6a90626295",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}