{
  "annotation_id": "76dc58e8-97c1-4a74-aa6e-ced536537924",
  "date_created": "2026-03-02T18:02:34.665000Z",
  "date_modified": "2026-03-02T18:02:34.665000Z",
  "file_hash": "8bbd9bfef5ade5d7dcdd0fd0aaf6b565375c2258cb1a39a52ba83ca2fbc29bad",
  "private": false,
  "record": {
    "abstract": "Krawtchouk\u0027s polynomials occur classically as orthogonal polynomials with\nrespect to the binomial distribution. They may be also expressed in the form of\nmatrices, that emerge as arrays of the values that the polynomials take. The\nalgebraic properties of these matrices provide a very interesting and\naccessible example in the approach to probability theory known as quantum\nprobability. First it is noted how the Krawtchouk matrices are connected to the\nclassical symmetric Bernoulli random walk. And we show how to derive Krawtchouk\nmatrices in the quantum probability context via tensor powers of the elementary\nHadamard matrix. Then connections with the classical situation are shown by\ncalculating expectation values in the quantum case.",
    "arxiv_id": "quant-ph/0702173",
    "authors": [
      "Philip Feinsilver",
      "Jerzy Kocik"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Contemporary Mathematics, Volume 287 (2001) 83-96",
    "title": "Krawtchouk matrices from classical and quantum random walks",
    "url": "https://arxiv.org/abs/quant-ph/0702173"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a9389dc9-f19c-44c7-81a7-e570c3fa6211",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}