{
  "annotation_id": "83d4d1c9-a6cc-4d6a-8295-528b729a5305",
  "date_created": "2026-03-02T18:02:41.652000Z",
  "date_modified": "2026-03-02T18:02:41.652000Z",
  "file_hash": "938b2a16b5451b85394205aa2f4f68cf07a433d2e30ac5c80794ddb8f07b53b3",
  "private": false,
  "record": {
    "abstract": "We first present a useful characterization of additive (stabilizer) quantum\nerror-correcting codes. Then we present several examples of We first present a\nuseful characterization of additive (stabilizer) quantum error--correcting\ncodes. Then we present several examples of nonadditive codes. We show that\nthere exist infinitely many non-trivial nonadditive codes with different\nminimum distances, and high rates. In fact, we show that nonadditive codes that\ncorrect t errors can reach the asymptotic rate R=1-2H(2t/n), where H(x) is the\nbinary entropy function. Finally, we introduce the notion of strongly\nnonadditive codes (i.e., quantum codes with the following property: the trivial\ncode consisting of the entire Hilbert space is the only additive code that is\nequivalent to any code containing the given code), and provide a construction\nfor an ((11,2,3)) strongly nonadditive code.",
    "arxiv_id": "quant-ph/9710031",
    "authors": [
      "Vwani P. Roychowdhury",
      "Farrokh Vatan"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the Structure of Additive Quantum Codes and the Existence of   Nonadditive Codes",
    "url": "https://arxiv.org/abs/quant-ph/9710031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "85c8003c-1a10-4cf5-9bd2-5305a82cfc2b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}