{
  "annotation_id": "30eb8c12-4300-4e3c-9b72-d30b8f6e0d9e",
  "date_created": "2026-03-02T18:02:48.053000Z",
  "date_modified": "2026-03-02T18:02:48.053000Z",
  "file_hash": "43679b055258f89b1bb03212dbdb7d2c449c6717915aafdf46551dd37a439127",
  "private": false,
  "record": {
    "abstract": "In Part II we show that there exist quantum codes whose probability of\nundetected error falls exponentially with the length of the code and derive\nbounds on this exponent.The lower (existence) bound for stabilizer codes is\nproved by a counting argument for classical self-orthogonal quaternary codes.\nUpper bounds for any quantum codes are proved by linear programming. We present\ntwo general solutions of the LP problem. Together they give an upper bound on\nthe exponent of undetected error. The upper and lower asymptotic bounds\ncoincide for a certain interval of code rates close to 1.",
    "arxiv_id": "quant-ph/9906131",
    "authors": [
      "A. Ashikhmin",
      "A. Barg",
      "E. Knill",
      "S. Litsyn"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Error Detection II: Bounds",
    "url": "https://arxiv.org/abs/quant-ph/9906131"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "82bd7219-6f2d-4230-8ccf-af83d664f93b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}