{
  "id": "quant-ph/0001066",
  "version": "v3",
  "published": "2000-01-18T14:38:34.000Z",
  "updated": "2005-11-20T12:21:01.000Z",
  "title": "Efficient factorization with a single pure qubit and $log N$ mixed qubits",
  "authors": [
    "S. Parker",
    "M. B. Plenio"
  ],
  "comment": "5 pages including 2 figures. Final version submitted to PRL. Now includes additional comments on entanglement and mixedness as algorithm proceeds. Added references to work by Mosca",
  "journal": "Phys. Rev. Lett. 85, 3049 (2000)",
  "doi": "10.1103/PhysRevLett.85.3049",
  "categories": [
    "quant-ph"
  ],
  "abstract": "It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an arbitrary mixed state is sufficient to implement Shor's factorization algorithm efficiently.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-11-20T12:21:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "single pure qubit",
      "efficient factorization",
      "mixed qubits",
      "shors quantum algorithm",
      "implement shors factorization algorithm"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}