{
  "annotation_id": "07d0e853-6164-47a4-a865-93278fb473d1",
  "date_created": "2026-03-02T18:01:52.498000Z",
  "date_modified": "2026-03-02T18:01:52.498000Z",
  "file_hash": "149cf868265aecb921193ee25f297d4c34f6d18b6a8ec829ad763ea15874a8f6",
  "private": false,
  "record": {
    "abstract": "This letter treats the quantum random walk on the line determined by a 2\ntimes 2 unitary matrix U. A combinatorial expression for the mth moment of the\nquantum random walk is presented by using 4 matrices, P, Q, R and S given by U.\nThe dependence of the mth moment on U and initial qubit state phi is clarified.\nA new type of limit theorems for the quantum walk is given. Furthermore\nnecessary and sufficient conditions for symmetry of distribution for the\nquantum walk is presented. Our results show that the behavior of quantum random\nwalk is striking different from that of the classical ramdom walk.",
    "arxiv_id": "quant-ph/0206053",
    "authors": [
      "Norio Konno"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Information Processing, Vol.1, Issue 5, pp.345-354 (2002)",
    "title": "Quantum random walks in one dimension",
    "url": "https://arxiv.org/abs/quant-ph/0206053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cec0c6b8-045f-49ad-bb4d-d044c490cab1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}