{
  "annotation_id": "506b141a-d77f-4a78-a0d0-897bbac60568",
  "date_created": "2026-03-02T18:02:41.479000Z",
  "date_modified": "2026-03-02T18:02:41.479000Z",
  "file_hash": "55f49461bc94db430d8ad90c00cf6533fd7cb0dab867c16b8cdae0784d59eb9d",
  "private": false,
  "record": {
    "abstract": "We present a family of additive quantum error-correcting codes whose\ncapacities exceeds that of quantum random coding (hashing) for very noisy\nchannels. These codes provide non-zero capacity in a depolarizing channel for\nfidelity parameters $f$ when $f\u003e .80944$. Random coding has non-zero capacity\nonly for $f\u003e.81071$; by analogy to the classical Shannon coding limit, this\nvalue had previously been conjectured to be a lower bound. We use the method\nintroduced by Shor and Smolin of concatenating a non-random (cat) code within a\nrandom code to obtain good codes. The cat code with block size five is shown to\nbe optimal for single concatenation. The best known multiple-concatenated code\nwe found has a block size of 25. We derive a general relation between the\ncapacity attainable by these concatenation schemes and the coherent information\nof the inner code states.",
    "arxiv_id": "quant-ph/9706061",
    "authors": [
      "David P. DiVincenzo",
      "Peter W. Shor",
      "John A. Smolin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.57.830",
    "title": "Quantum Channel Capacity of Very Noisy Channels",
    "url": "https://arxiv.org/abs/quant-ph/9706061"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "435d71de-85aa-42d6-90b3-8f7bcf5de5ea",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}