{
  "annotation_id": "d414b217-a05f-4bbb-b6c2-fdcaaead5b6f",
  "date_created": "2026-03-02T18:01:52.999000Z",
  "date_modified": "2026-03-02T18:01:52.999000Z",
  "file_hash": "3310bfa0f16bcf52f26ce0e0f082eb4ec6a581589807f15d528514d89571c571",
  "private": false,
  "record": {
    "abstract": "In this paper we consider the one-dimensional quantum random walk X^{varphi}\n_n at time n starting from initial qubit state varphi determined by 2 times 2\nunitary matrix U. We give a combinatorial expression for the characteristic\nfunction of X^{varphi}_n. The expression clarifies the dependence of it on\ncomponents of unitary matrix U and initial qubit state varphi. As a consequence\nof the above results, we present a new type of limit theorems for the quantum\nrandom walk. In contrast with the de Moivre-Laplace limit theorem, our\nsymmetric case implies that X^{varphi}_n /n converges in distribution to a\nlimit Z^{varphi} as n to infty where Z^{varphi} has a density 1 / pi (1-x^2)\nsqrt{1-2x^2} for x in (- 1/sqrt{2}, 1/sqrt{2}). Moreover we discuss some known\nsimulation results based on our limit theorems.",
    "arxiv_id": "quant-ph/0206103",
    "authors": [
      "Norio Konno"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Journal of the Mathematical Society of Japan, Vol.57, No.4,\n  pp.1179-1195 (2005)",
    "title": "A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk",
    "url": "https://arxiv.org/abs/quant-ph/0206103"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2fe87f82-9a00-4191-8d9d-ac92ad6db596",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}