{
  "id": "1901.10665",
  "version": "v1",
  "published": "2019-01-30T04:13:15.000Z",
  "updated": "2019-01-30T04:13:15.000Z",
  "title": "Time operators for continuous-time and discrete-time quantum walks",
  "authors": [
    "Daiju Funakawa",
    "Yasumichi Matsuzawa",
    "Akito Suzuki",
    "Itaru Sasaki",
    "Noriaki Teranishi"
  ],
  "comment": "12pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study time operators for both continuous and discrete-time quantum walks. Because the continuous-time quantum has a Hamiltonian, we can define its time operators by the canonical commutation relation to the Hamiltonian. On the other hand, the discrete-time quantum walk has no Hamiltonian and its evolution is described by a unitary operator. Hence, it is natural to define the time operators for the iscrete-time quantum walk by a commutation relation to the unitary operator. In this paper, we construct concrete examples of the time operators for both continuous and discrete-time quantum walks. We also separate time operators for a unitary operator into two classes and give their basic properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-30T04:13:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete-time quantum walk",
      "unitary operator",
      "commutation relation",
      "separate time operators",
      "construct concrete examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}