{
  "annotation_id": "e07a68b8-91b8-4dd1-8113-04bef9fc3433",
  "date_created": "2026-03-02T18:02:19.359000Z",
  "date_modified": "2026-03-02T18:02:19.359000Z",
  "file_hash": "162c0b70b4b9e87953afc1f2f509a50429f0071055615bd26a7607124b6c988d",
  "private": false,
  "record": {
    "abstract": "We study a generalized Hadamard walk in one dimension with three inner\nstates. The particle governed by the three-state quantum walk moves, in\nsuperposition, both to the left and to the right according to the inner state.\nIn addition to these two degrees of freedom, it is allowed to stay at the same\nposition. We calculate rigorously the wavefunction of the particle starting\nfrom the origin for any initial qubit state, and show the spatial distribution\nof probability of finding the particle. In contrast with the Hadamard walk with\ntwo inner states on a line, the probability of finding the particle at the\norigin does not converge to zero even after infinite time steps except special\ninitial states. This implies that the particle is trapped near the origin after\nlong time with high probability.",
    "arxiv_id": "quant-ph/0507207",
    "authors": [
      "Norio Inui",
      "Norio Konno",
      "Etsuo Segawa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevE.72.056112",
    "title": "One-Dimensional Three-State Quantum Walk",
    "url": "https://arxiv.org/abs/quant-ph/0507207"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7862ec00-0d87-4f82-9e47-478e39c842e4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}