{
  "id": "1301.1166",
  "version": "v1",
  "published": "2013-01-07T12:24:27.000Z",
  "updated": "2013-01-07T12:24:27.000Z",
  "title": "Quantum channels from association schemes",
  "authors": [
    "Tao Feng",
    "Simone Severini"
  ],
  "comment": "6 pages",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We propose in this note the study of quantum channels from association schemes. This is done by interpreting the $(0,1)$-matrices of a scheme as the Kraus operators of a channel. Working in the framework of one-shot zero-error information theory, we give bounds and closed formulas for various independence numbers of the relative non-commutative (confusability) graphs, or, equivalently, graphical operator systems. We use pseudocyclic association schemes as an example. In this case, we show that the unitary entanglement-assisted independence number grows at least quadratically faster, with respect to matrix size, than the independence number. The latter parameter was introduced by Beigi and Shor as a generalization of the one-shot Shannon capacity, in analogy with the corresponding graph-theoretic notion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-07T12:24:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum channels",
      "unitary entanglement-assisted independence number grows",
      "one-shot zero-error information theory",
      "one-shot shannon capacity",
      "pseudocyclic association schemes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1166F"
    }
  }
}