{
  "id": "1503.05342",
  "version": "v1",
  "published": "2015-03-18T11:08:07.000Z",
  "updated": "2015-03-18T11:08:07.000Z",
  "title": "Beyond Complete Positivity",
  "authors": [
    "Jason M. Dominy",
    "Daniel A. Lidar"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any C-linear, Hermiticity- preserving, trace-preserving subsystem map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-18T11:08:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete positivity",
      "linear subsystem quantum dynamical maps",
      "joint system-bath unitary evolutions",
      "joint unitary evolution",
      "quantum data processing inequality"
    ],
    "publication": {
      "doi": "10.1007/s11128-015-1228-1",
      "journal": "Quantum Information Processing",
      "year": 2016,
      "month": "Apr",
      "volume": 15,
      "number": 4,
      "pages": 1349
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016QuIP...15.1349D"
    }
  }
}