{
  "id": "1710.01482",
  "version": "v1",
  "published": "2017-10-04T07:01:42.000Z",
  "updated": "2017-10-04T07:01:42.000Z",
  "title": "Probability distributions of quaternionic quantum walks",
  "authors": [
    "Kei Saito"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "quant-ph",
    "math.PR"
  ],
  "abstract": "The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The probability distribution of a class of QQWs is the same as that of the QW. On the other hand, a numerical simulation suggests that the probability distribution of a QQW is different from the QW. In this paper, we clarify the difference between the QQW and the QW by weak limit theorems for a class of QQWs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-04T07:01:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "81P68"
    ],
    "keywords": [
      "probability distribution",
      "model quaternionic quantum walk",
      "discrete-time quantum walk",
      "weak limit theorems",
      "unitary matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}