{
  "id": "1309.5898",
  "version": "v3",
  "published": "2013-09-23T17:58:25.000Z",
  "updated": "2014-10-29T13:58:56.000Z",
  "title": "On the extreme points of quantum channels",
  "authors": [
    "Shmuel Friedland",
    "Raphael Loewy"
  ],
  "comment": "Slightly revised version, 19 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Let L(m,n) denote the convex set of completely positive trace preserving operators from C^{m x m} to C^{n x n}$, i.e quantum channels. We give a necessary condition for L in L(m,n) to be an extreme point. We show that generically, this condition is also sufficient. We characterize completely the extreme points of L_(2,2) and L(3,2), i.e. quantum channels from qubits to qubits and from qutrits to qubits.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-21T16:48:30.000Z",
      "comment": "Significantly revised version, 20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-29T13:58:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B48",
      "47B65",
      "94A17",
      "94A40"
    ],
    "keywords": [
      "quantum channels",
      "extreme point",
      "positive trace preserving operators",
      "necessary condition",
      "convex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5898F"
    }
  }
}