{
  "annotation_id": "61627ebf-b127-4a32-9791-3fa4a80fc8c3",
  "date_created": "2026-03-02T18:01:38.672000Z",
  "date_modified": "2026-03-02T18:01:38.672000Z",
  "file_hash": "2503eb4be1b2a870c7437c839c1593de673dc72f9c8d33fd14afdd84f3099425",
  "private": false,
  "record": {
    "abstract": "The Schmidt number of a mixed state characterizes the minimum Schmidt rank of\nthe pure states needed to construct it. We investigate the Schmidt number of an\narbitrary mixed state by constructing a Schmidt number witness that detects it.\nWe present a canonical form of such witnesses and provide constructive methods\nfor their optimization. Finally, we present strong evidence that all bound\nentangled states with positive partial transpose in two qutrit systems have\nSchmidt number 2.",
    "arxiv_id": "quant-ph/0009109",
    "authors": [
      "Anna Sanpera",
      "Dagmar Bruss",
      "Maciej Lewenstein"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.63.050301",
    "journal_ref": "Phys. Rev. A 63, 050301 (2001)",
    "title": "Schmidt number witnesses and bound entanglement",
    "url": "https://arxiv.org/abs/quant-ph/0009109"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3eb8480e-ea90-4611-a74c-b282f26d5652",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}