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Noncommutative Poisson boundaries of unital quantum operations. (English) Zbl 1310.81019
Summary: 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 A. Arias et al. [ibid. 43, No. 12, 5872–5881 (2002; Zbl 1060.81009)] about injectivity of the commuting algebra of the Kraus operators of unital quantum operations and their injective envelopes.
©2010 American Institute of Physics

81P15 Quantum measurement theory, state operations, state preparations
81S25 Quantum stochastic calculus
46L07 Operator spaces and completely bounded maps
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H10 Fixed-point theorems
46L10 General theory of von Neumann algebras
46L60 Applications of selfadjoint operator algebras to physics
Full Text: DOI
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