{
  "id": "1507.08404",
  "version": "v1",
  "published": "2015-07-30T07:11:56.000Z",
  "updated": "2015-07-30T07:11:56.000Z",
  "title": "Irreducible decompositions and stationary states of quantum channels",
  "authors": [
    "Raffaella Carbone",
    "Yan Pautrat"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a general quantum channel into its irreducible positive recurrent components. This decomposition is related with a communication relation on the reference Hilbert space. This allows us to describe the full structure of invariant states of a quantum channel, and of their supports.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-30T07:11:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary states",
      "irreducible decompositions",
      "infinite dimensional case",
      "general quantum channel",
      "reference hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708404C"
    }
  }
}