{
  "annotation_id": "684a1424-0a0e-4829-b976-414ca9a05777",
  "date_created": "2026-03-02T18:01:56.614000Z",
  "date_modified": "2026-03-02T18:01:56.614000Z",
  "file_hash": "c5500bc9dd6172746b2667b7a18b7fedd5dd82b04059200a42daf84b7d65e9a2",
  "private": false,
  "record": {
    "abstract": "We prove a lower bound for Schmidt numbers of bipartite mixed states. This\nlower bound can be applied easily to low rank bipartite mixed states. From this\nlower bound it is known that generic low rank bipartite mixed states have\nrelatively high Schmidt numbers and thus entangled. We can compute Schmidt\nnumbers exactly for some mixed states by this lower bound as shown in Examples.\nThis lower bound can also be used effectively to determine that some mixed\nstates cannot be convertible to other mixed states by local operations and\nclassical communication.\n  The results in this paper are proved by ONLY using linear algebra, thus the\nresults and proof are easy to understand.",
    "arxiv_id": "quant-ph/0211052",
    "authors": [
      "Hao Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.67.062301",
    "title": "Schmidt numbers of low rank bipartite mixed states",
    "url": "https://arxiv.org/abs/quant-ph/0211052"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3767745f-5d96-4583-bc0d-0982b9cee5ef",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}