{
  "annotation_id": "dd999013-7a7c-414c-a396-1f743ebb4245",
  "date_created": "2026-03-02T18:01:56.507000Z",
  "date_modified": "2026-03-02T18:01:56.507000Z",
  "file_hash": "cf8be706e06b7cb079faa9288aa48c9e70c635bf64fce6420055945a65959b6a",
  "private": false,
  "record": {
    "abstract": "The recent proposed realignment separability criterion for mixed is analyzed.\nWe identify the essential part of this criterion is a swap operator followed by\na partial transposition. Then we analyze the separability criterion of\npermutation indices of the density matrix for multipartite state which is a\ngeneralization of the realignment criterion. We give a method to solve the\nequivalence problem of the separability criterion of permutation indices of the\ndensity matrix. For tripartite state, we show the non-trivial separability\ncriteria are either partial transposition criterion or realignment criterion.",
    "arxiv_id": "quant-ph/0210168",
    "authors": [
      "Heng Fan"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A note on separability criteria for multipartite state",
    "url": "https://arxiv.org/abs/quant-ph/0210168"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4f06b108-765c-4a5f-9632-5ea5bf0fe0ec",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}