{
  "annotation_id": "fa88a3e9-159b-4896-bb36-bee6e7260120",
  "date_created": "2026-03-02T18:02:48.054000Z",
  "date_modified": "2026-03-02T18:02:48.054000Z",
  "file_hash": "82d66ea07b7442d238ff45caa52861e9aee05fb881b4160ef9883868c3b7c7e1",
  "private": false,
  "record": {
    "abstract": "I. This paper is devoted to the problem of error detection with quantum\ncodes. In the first part we examine possible problem settings for quantum error\ndetection. Our goal is to derive a functional that describes the probability of\nundetected error under natural physical assumptions concerning transmission\nwith error detection over the depolarizing channel. We discuss possible\ntransmission protocols with stabilizer and unrestricted quantum codes. The set\nof results proved in Part I shows that in all the cases considered the average\nprobability of undetected error for a given code is essentially given by one\nand the same function of its weight enumerators. This enables us to give a\nconsistent definition of the undetected error event.",
    "arxiv_id": "quant-ph/9906126",
    "authors": [
      "Alexei Ashikhmin",
      "Alexander Barg",
      "Emanuel Knill",
      "Simon Litsyn"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Error Detection I: Statement of the Problem",
    "url": "https://arxiv.org/abs/quant-ph/9906126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3fb48f78-b6bd-433b-9837-d66b496c04e2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}