id: 06031188
dt: a
an: 06031188
au: Belavkin, Viacheslav P.
ti: New types of quantum entropies and additive information capacities.
so: Accardi, Luigi (ed.) et al., Quantum bio-informatics IV. From quantum
    information to bio-informatics, Tokyo, Japan, March 10‒13, 2010.
    Selected papers based on the presentations at the international
    conference. Hackensack, NJ: World Scientific (ISBN
    978-981-4343-75-6/hbk; 978-981-4343-76-3/ebook). QP-PQ: Quantum
    Probability and White Noise Analysis 28, 61-89 (2011).
py: 2011
pu: Hackensack, NJ: World Scientific
la: EN
cc: 
ut: quantum channel capacities; quantum divergence; mutual information
ci: 
li: http://ebooks.worldscinet.com/ISBN/9789814343763/9789814343763_0006.html
ab: An elementary algebraic approach to unified quantum information theory is
    given. An operational meaning of entanglement as specifically quantum
    encoding is disclosed. The general relative entropy as information
    divergence is introduced and three most important types of relative
    information, namely, Araki-Umegaki (A-type) and of Belavkin-Staszewski
    (B-type) and the thermodynamical (C-type) are described. The true
    quantum entropy different from the von Neumann semiclassical entropy is
    introduced and the proper quantum conditional entropy is proposed. The
    general quantum mutual information via entanglement is defined and the
    corresponding types of quantum channel capacities as the supremum via
    the generalized encodings are formulated. The additivity problem for
    quantum logarithmic capacities for the products of arbitrary quantum
    channels under the appropriate constraints on encodings is discussed.
    It is proved that the true quantum capacity, which is achieved on the
    standard entanglement as the optimal quantum encoding, reclaims the
    additivity property of the logarithmic quantum channel capacities via
    the entanglement on the products of quantum input states. This earlier
    obtained by V. P. B. result for quantum logarithmic information of
    A-type is extended to any type of quantum information.  The paper is
    organized as follows: section two introduces related notions of quantum
    probability and information theory, such as quantum state and quantum
    entanglement; section three introduces the general quantum divergence
    and new types of quantum relative entropies via the divergence; section
    four introduces the entangled quantum mutual information and the true
    quantum entropies of three types achieved via entanglement; section
    five introduces quantum channel capacity via entanglement encoding and
    shows additivity of the logarithmic entangled quantum channel capacity
    of any type; the final section contributes to conclusion and further
    problems.
rv: Vladislav Nikolaevich Dumachev (Voronezh)