{
  "annotation_id": "716d451e-5941-4ae8-9bb2-8ac17b2aac85",
  "date_created": "2026-03-02T18:02:02.923000Z",
  "date_modified": "2026-03-02T18:02:02.923000Z",
  "file_hash": "974532ce973f93900fba73a35b6046cdd10a74e21b90186c51ce2e47f0a23c40",
  "private": false,
  "record": {
    "abstract": "We analyze the solution of the coined quantum walk on a line. First, we\nderive the full solution, for arbitrary unitary transformations, by using a new\napproach based on the four \"walk fields\" which we show determine the dynamics.\nThe particular way of deriving the solution allows a rigorous derivation of a\nlong wavelength approximation. This long wavelength approximation is useful as\nit provides an approximate analytical expression that captures the basics of\nthe quantum walk and allows us to gain insight into the physics of the process.",
    "arxiv_id": "quant-ph/0312133",
    "authors": [
      "P. L. Knight",
      "E. Roldan",
      "J. E. Sipe"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1080/09500340408232489",
    "journal_ref": "J. Mod. Opt. 51 (2004) 1761-1777",
    "title": "Propagating Quantum Walks: the origin of interference structures",
    "url": "https://arxiv.org/abs/quant-ph/0312133"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8196b43e-d7c4-4e07-9710-1dde0b72a83c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}