{
  "annotation_id": "c201c14b-4167-49e8-a347-ef11e21ddfbb",
  "date_created": "2026-03-02T18:02:37.923000Z",
  "date_modified": "2026-03-02T18:02:37.923000Z",
  "file_hash": "702ed6631585f3e403176b82b33579f8270b32183a648935b6b6d2b8901fcb57",
  "private": false,
  "record": {
    "abstract": "An $n$-bit string is encoded as a sequence of non-orthogonal quantum states.\nThe parity bit of that $n$-bit string is described by one of two density\nmatrices, $\\rho_0^{(n)}$ and $\\rho_1^{(n)}$, both in a Hilbert space of\ndimension $2^n$. In order to derive the parity bit the receiver must\ndistinguish between the two density matrices, e.g., in terms of optimal mutual\ninformation. In this paper we find the measurement which provides the optimal\nmutual information about the parity bit and calculate that information. We\nprove that this information decreases exponentially with the length of the\nstring in the case where the single bit states are almost fully overlapping. We\nbelieve this result will be useful in proving the ultimate security of quantum\ncrytography in the presence of noise.",
    "arxiv_id": "quant-ph/9604040",
    "authors": [
      "C. H. Bennett",
      "T. Mor",
      "J. A. Smolin"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.54.2675",
    "title": "The Parity Bit in Quantum Cryptography",
    "url": "https://arxiv.org/abs/quant-ph/9604040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b515995e-2d17-42e9-8bf4-ceefccc3ef0a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}