{
  "id": "quant-ph/0208111",
  "version": "v1",
  "published": "2002-08-15T22:47:10.000Z",
  "updated": "2002-08-15T22:47:10.000Z",
  "title": "Entanglement, Quantum Entropy and Mutual Information",
  "authors": [
    "V. P. Belavkin",
    "M. Ohya"
  ],
  "comment": "23 pages, see also related publications at http://www.maths.nott.ac.uk/personal/vpb/vpb_research.html",
  "journal": "Proc. R. Soc. Lond. A 458 (2002) 209--231",
  "doi": "10.1098/rspa.2001.0867",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The operational structure of quantum couplings and entanglements is studied and classified for semifinite von Neumann algebras. We show that the classical-quantum correspondences such as quantum encodings can be treated as diagonal semi-classical (d-) couplings, and the entanglements characterized by truly quantum (q-) couplings, can be regarded as truly quantum encodings. The relative entropy of the d-compound and entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the maximum of mutual information over all d-entanglements, and the dimensional entropy, which is achieved at the standard entanglement -- true quantum entanglement, coinciding with a d-entanglement only in the case of pure marginal states. The d- and q- information of a quantum noisy channel are respectively defined via the input d- and q- encodings, and the q-capacity of a quantum noiseless channel is found as the logarithm of the dimensionality of the input algebra. The quantum capacity may double the classical capacity, achieved as the supremum over all d-couplings, or encodings, bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-08-15T22:47:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutual information",
      "quantum entropy",
      "semifinite von neumann algebras",
      "von neumann entropy",
      "true quantum entanglement"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}