{
  "annotation_id": "6ff99d49-9f93-4637-8aa8-7050b978f81a",
  "date_created": "2026-03-02T18:01:52.563000Z",
  "date_modified": "2026-03-02T18:01:52.563000Z",
  "file_hash": "389363501ac59b3319a78c7e45febfc91d7753904db4373719985b8819941643",
  "private": false,
  "record": {
    "abstract": "We first propose a new separability criterion based on algebraic-geometric\ninvariants of bipartite mixed states introduced in [1], then prove that for all\nlow ranks r \u003cm+n-2, generic rank r mixed states in mxn systems have relatively\nhigh Schmidt numbers (thus entangled) by this separability criterion. This also\nmeans that the algebraic-geometric separability criterion proposed here can be\nused to dectect all low rank entangled mixed states outside a measure zero set.",
    "arxiv_id": "quant-ph/0207130",
    "authors": [
      "Hao Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Algebraic-geometric separability criterion and low rank mixed state   entanglement",
    "url": "https://arxiv.org/abs/quant-ph/0207130"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "158d1edd-aa5c-47f2-a40f-bf04d5c875dd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}