{
  "annotation_id": "20a71952-fdaf-490c-bede-2cfcf369c6d9",
  "date_created": "2026-03-02T18:01:53.047000Z",
  "date_modified": "2026-03-02T18:01:53.047000Z",
  "file_hash": "2c11cd72a8ece7f1bca1227a468f857cb339fae331c9d0bd0b87bf3398a4d361",
  "private": false,
  "record": {
    "abstract": "In this paper we analyze the behavior of quantum random walks. In particular\nwe present several new results for the absorption probabilities in systems with\nboth one and two absorbing walls for the one-dimensional case. We compute these\nprobabilites both by employing generating functions and by use of an\neigenfunction approach. The generating function method is used to determine\nsome simple properties of the walks we consider, but appears to have\nlimitations. The eigenfunction approach works by relating the problem of\nabsorption to a unitary problem that has identical dynamics inside a certain\ndomain, and can be used to compute several additional interesting properties,\nsuch as the time dependence of absorption. The eigenfunction method has the\ndistinct advantage that it can be extended to arbitrary dimensionality. We\noutline the solution of the absorption probability problem of a\n(d-1)-dimensional wall in a d-dimensional space.",
    "arxiv_id": "quant-ph/0207008",
    "authors": [
      "Eric Bach",
      "Susan Coppersmith",
      "Marcel Paz Goldschen",
      "Robert Joynt",
      "John Watrous"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "One-dimensional quantum walks with absorbing boundaries",
    "url": "https://arxiv.org/abs/quant-ph/0207008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "46f42e00-87f3-4ffb-83a4-1824d8f3caf9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}