{
  "annotation_id": "054b8c35-d761-49dd-9bc6-5fbaf4c52627",
  "date_created": "2026-03-02T18:02:05.748000Z",
  "date_modified": "2026-03-02T18:02:05.748000Z",
  "file_hash": "d22a8469cc4b22b5da6ede93ab0547aea24a3b68e7d4087f81dba52dd704ec96",
  "private": false,
  "record": {
    "abstract": "We apply the generalised concept of witness operators to arbitrary convex\nsets, and review the criteria for the optimisation of these general witnesses.\nWe then define an embedding of state vectors and operators into a\nhigher-dimensional Hilbert space. This embedding leads to a connection between\nany Schmidt number witness in the original Hilbert space and a witness for\nSchmidt number two (i.e. the most general entanglement witness) in the\nappropriate enlarged Hilbert space. Using this relation we arrive at a\nconceptually simple method for the construction of Schmidt number witnesses in\nbipartite systems.",
    "arxiv_id": "quant-ph/0401118",
    "authors": [
      "Florian Hulpke",
      "Dagmar Bruss",
      "Maciej Lewenstein",
      "Anna Sanpera"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quant. Inf. Comp. 4, 207 (2004)",
    "title": "Simplifying Schmidt number witnesses via higher-dimensional embeddings",
    "url": "https://arxiv.org/abs/quant-ph/0401118"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "42db66e4-e501-475f-ab02-a42b16574b2f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}