{
  "id": "quant-ph/0501142",
  "version": "v3",
  "published": "2005-01-25T01:18:37.000Z",
  "updated": "2005-06-30T23:29:49.000Z",
  "title": "On Randomized and Quantum Query Complexities",
  "authors": [
    "Gatis Midrijanis"
  ],
  "comment": "10 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$ for any total function $f$, where $D(f)$ is the minimal number of queries made by a deterministic query algorithm and $Q_1(f)$ is the number of queries made by any quantum query algorithm (decision tree analog in quantum case) with one-sided constant error; both algorithms compute function $f$. Secondly, we show that for all total Boolean functions $f$ holds $R_0(f)=O(R_2(f)^2 \\log N)$, where $R_0(f)$ and $R_2(f)$ are randomized zero-sided (a.k.a Las Vegas) and two-sided (a.k.a. Monte Carlo) error query complexities.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-30T23:29:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complexity",
      "quantum query complexities",
      "total boolean functions",
      "quantum query algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005quant.ph..1142M"
    }
  }
}