Noncommutative Poisson boundaries of unital quantum operations

Journal Article · Sat May 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3407600· OSTI ID:21335955

Lim, Bunrith Jacques ^[1]

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1. Institut de Recherche Mathematique de Rennes (IRMAR), Universite de Rennes 1 and CNRS (UMR 6625), 35042 Rennes Cedex (France)

In this paper, Poisson boundaries of unital quantum operations (also called Markov operators) are investigated. In the case of unital quantum channels, compact operators belonging to Poisson boundaries are characterized. Using the characterization of amenable groups by the injectivity of their von Neumann algebras, we will answer negatively some conjectures appearing in the work of Arias et al. ['Fixed points of quantum operations', J. Math. Phys. 43, 5872 (2002)] about injectivity of the commuting algebra of the Kraus operators of unital quantum operations and their injective envelopes.

• OSTI ID: 21335955
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 5; Other Information: DOI: 10.1063/1.3407600; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
MARKOV PROCESS
QUANTUM COMPUTERS
QUANTUM MECHANICS