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Poisson boundaries of quantum operations and quantum trajectories

Abstract : The study of this thesis takes place in the mathematical foundations of quantum information theory and quantum physics, through the study of the set of fixed points (also called Poisson boundary) of a quantum operation, and the study of quantum trajectories in infinite dimension. At first, we precise the Poisson boundary of quantum operations. Then we answer negatively some conjectures appearing in the work of Arias et al. concerning Poisson boundaries of quantum operations. In second place, we identify the noncommutative Poisson boundary on a s-discrete measured groupoid. This identification enables us to give another proof of the amenability of the Poisson extension of the groupoid. At last, results concerning asymptotic purification of quantum trajectories taking values in a strongly compact algebra are obtained.
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Submitted on : Wednesday, November 2, 2011 - 3:25:51 PM
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  • HAL Id : tel-00637636, version 1


Bunrith Jacques Lim. Poisson boundaries of quantum operations and quantum trajectories. Mathematics [math]. Université Rennes 1, 2010. English. ⟨tel-00637636⟩



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