{
  "id": "0811.0947",
  "version": "v1",
  "published": "2008-11-06T13:52:07.000Z",
  "updated": "2008-11-06T13:52:07.000Z",
  "title": "The multiplicative domain in quantum error correction",
  "authors": [
    "Man-Duen Choi",
    "Nathaniel Johnston",
    "David W. Kribs"
  ],
  "comment": "17 pages, preprint version",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of the recovery process, the so-called unitarily correctable codes. Whereas in the arbitrary, not necessarily unital case they form a proper subset of unitarily correctable codes that can be computed from properties of the channel. As part of the analysis we derive a representation theoretic characterization of subsystem codes. We also present a number of illustrative examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-06T13:52:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum error correction",
      "multiplicative domain",
      "unitarily correctable codes",
      "quantum error correcting codes",
      "unital quantum channel"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/42/24/245303",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Jun",
      "volume": 42,
      "number": 24,
      "pages": 245303
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42x5303C"
    }
  }
}