{
  "id": "quant-ph/0012111",
  "version": "v1",
  "published": "2000-12-20T16:20:53.000Z",
  "updated": "2000-12-20T16:20:53.000Z",
  "title": "Quantum error-correcting codes associated with graphs",
  "authors": [
    "D. Schlingemann",
    "R. F. Werner"
  ],
  "comment": "8 pages revtex, 5 figures",
  "doi": "10.1103/PhysRevA.65.012308",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math-ph",
    "math.IT",
    "math.MP"
  ],
  "abstract": "We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-12-20T16:20:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum error-correcting codes",
      "quantum error correcting codes",
      "finite abelian group",
      "basic ingredients",
      "tenfold code"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}