{
  "id": "quant-ph/0008011",
  "version": "v1",
  "published": "2000-08-02T19:48:43.000Z",
  "updated": "2000-08-02T19:48:43.000Z",
  "title": "Universal Manipulation of a Single Qubit",
  "authors": [
    "Lucien Hardy",
    "David D. Song"
  ],
  "comment": "6 pages, 1 figure",
  "journal": "Phys. Rev. A 63, 032304 (2001)",
  "doi": "10.1103/PhysRevA.63.032304",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We find the optimal universal way of manipulating a single qubit, |psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather surprising that for some values of k the fidelity is lower than 2/3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-08-02T19:48:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "single qubit",
      "universal manipulation",
      "optimal map",
      "fidelity varies",
      "optimal universal way"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}