{
  "id": "1103.3899",
  "version": "v4",
  "published": "2011-03-20T22:48:27.000Z",
  "updated": "2011-07-22T00:57:35.000Z",
  "title": "Limit Theorems For Quantum Walks Associated with Hadamard Matrices",
  "authors": [
    "Clement Ampadu"
  ],
  "journal": "Physical Review A, Volume 84, Number 1,012324 (2011)",
  "doi": "10.1103/PhysRevA.84.012324",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-07-22T00:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T25",
      "03.67.Ac"
    ],
    "keywords": [
      "quantum walks",
      "limit theorems",
      "hadamard matrices",
      "discrete-time quantum walk models",
      "hadamard walk"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2011,
      "month": "Jul",
      "volume": 84,
      "number": 1,
      "pages": "012324"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvA..84a2324A"
    }
  }
}