{
  "annotation_id": "5fed47dc-1fe5-4793-a3f3-089100b090c2",
  "date_created": "2026-03-02T18:02:44.645000Z",
  "date_modified": "2026-03-02T18:02:44.645000Z",
  "file_hash": "ceb39997935919f7ce531331de7e22c13a0d29c6e670b55cdab3f36f7fea0f1c",
  "private": false,
  "record": {
    "abstract": "An operator sum representation is derived for a decoherence-free subspace\n(DFS) and used to (i) show that DFSs are the class of quantum error correcting\ncodes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit\nrepresentations for the Kraus operators of collective decoherence. We\ndemonstrate how this can be used to construct a concatenated DFS-QECC code\nwhich protects against collective decoherence perturbed by independent\ndecoherence. The code yields an error threshold which depends only on the\nperturbing independent decoherence rate.",
    "arxiv_id": "quant-ph/9809081",
    "authors": [
      "D. A. Lidar",
      "D. Bacon",
      "K. B. Whaley"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevLett.82.4556",
    "journal_ref": "Phys.Rev.Lett. 82 (1999) 4556-4559",
    "title": "Concatenating Decoherence Free Subspaces with Quantum Error Correcting   Codes",
    "url": "https://arxiv.org/abs/quant-ph/9809081"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5a3578cc-a0e9-4a97-9fbe-66835e12fb8e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}