{
  "id": "1001.3828",
  "version": "v1",
  "published": "2010-01-21T15:33:14.000Z",
  "updated": "2010-01-21T15:33:14.000Z",
  "title": "Conditional expectations associated with quantum states",
  "authors": [
    "Gerd Niestegge"
  ],
  "comment": "10 pages, the original publication is available at http://www.aip.org",
  "journal": "2005 J. Math. Phys. 46, 043507",
  "doi": "10.1063/1.1861275",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations always exist; in the quantum case, however, they exist only if a certain weak compatibility criterion is satisfied. This compatibility criterion was introduced among others in a recent paper by the author. Then, state-independent conditional expectations and quantum Markov processes are studied. A classical Markov process is a probability measure, together with a system of random variables, satisfying the Markov property and can equivalently be described by a system of Markovian kernels (often forming a semigroup). This equivalence is partly extended to quantum probabilities. It is shown that a dynamical (semi)group can be derived from a given system of quantum observables satisfying the Markov property, and the group generators are studied. The results are presented in the framework of Jordan operator algebras, and a very general type of observables (including the usual real-valued observables or self-adjoint operators) is considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-21T15:33:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Fd",
      "02.50.Ga",
      "05.40.-a"
    ],
    "keywords": [
      "conditional expectations",
      "quantum states",
      "quantum case",
      "markov property",
      "observables"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2005,
      "month": "Apr",
      "volume": 46,
      "number": 4,
      "pages": "043507"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005JMP....46d3507N"
    }
  }
}