{
  "annotation_id": "94caad53-d957-4676-b5d1-69f2bb912386",
  "date_created": "2026-03-02T18:01:52.864000Z",
  "date_modified": "2026-03-02T18:01:52.864000Z",
  "file_hash": "0743ed3f6f3eb1805530d90070bc72744af82ac3de1f95b76024da32c9788874",
  "private": false,
  "record": {
    "abstract": "A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in\nsuch a way that one can recover any bit x_i from a corrupted codeword by\nquerying only a few bits of that word. We use a quantum argument to prove that\nLDCs with 2 classical queries need exponential length: m=2^{Omega(n)}.\nPreviously this was known only for linear codes (Goldreich et al. 02). Our\nproof shows that a 2-query LDC can be decoded with only 1 quantum query, and\nthen proves an exponential lower bound for such 1-query locally\nquantum-decodable codes. We also show that q quantum queries allow more\nsuccinct LDCs than the best known LDCs with q classical queries. Finally, we\ngive new classical lower bounds and quantum upper bounds for the setting of\nprivate information retrieval. In particular, we exhibit a quantum 2-server PIR\nscheme with O(n^{3/10}) qubits of communication, improving upon the O(n^{1/3})\nbits of communication of the best known classical 2-server PIR.",
    "arxiv_id": "quant-ph/0208062",
    "authors": [
      "Iordanis Kerenidis",
      "Ronald de Wolf"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "title": "Exponential Lower Bound for 2-Query Locally Decodable Codes via a   Quantum Argument",
    "url": "https://arxiv.org/abs/quant-ph/0208062"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "85321261-5eea-4fe7-bd59-6496b6160c56",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}