{
  "id": "quant-ph/0109158",
  "version": "v1",
  "published": "2001-09-28T18:09:34.000Z",
  "updated": "2001-09-28T18:09:34.000Z",
  "title": "Structure and Parametrization of Stochastic Maps of Density Matrices",
  "authors": [
    "E. C. G. Sudarshan"
  ],
  "comment": "10 pages, no figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable; but the positivity of the density matrix does not make this associated supermatrix positive. If it is positive, the map is called completely positive and they have a simple parametrization. This is extended to all positive (not completely positive) maps. A contraction of a norm-preserving map of the combined system can be contracted to obtain all dynamical maps. The reconstruction of the extended dynamics is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-09-28T18:09:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density matrix",
      "density matrices renders",
      "finite-dimensional state space",
      "dynamical stochastic maps form",
      "generic linear evolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001quant.ph..9158S"
    }
  }
}