{
  "id": "1804.10082",
  "version": "v1",
  "published": "2018-04-26T14:24:25.000Z",
  "updated": "2018-04-26T14:24:25.000Z",
  "title": "Comment on a classical limit of Grover's algorithm",
  "authors": [
    "Kazuo Fujikawa",
    "Koichiro Umetsu"
  ],
  "comment": "13 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A classical limit of Grover's algorithm is discussed by assuming a very rapid decoherence (or dephasing) between consecutive Grover's unitary operations, which leads pure quantum states to completely decohered mixed states. One can identify a specific element among $N$ unsorted elements by a probability of the order of unity after $k\\sim N/4$ steps of classical amplification defined by the decohered mixed states, in contrast to Grover's $k\\sim \\pi \\sqrt{N}/4$ steps in quantum mechanical amplification. This difference is caused by the loss of quantum coherence with or without the loss of entanglement depending on each case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-26T14:24:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grovers algorithm",
      "classical limit",
      "decohered mixed states",
      "pure quantum states",
      "consecutive grovers unitary operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}