# RECONSTRUCTION THEOREM FOR STATIONARY MONOTONE QUANTUM MARKOV PROCESSES

• Heo, Jae-Seong (Department of Mathematics Research Institute for Natural Sciences Hanyang University) ;
• Belavkin, Viacheslav P. (Mathematics Department University of Nottingham University Park) ;
• Ji, Un Cig (Department of Mathematics Research Institute of Mathematical Finance Chungbuk National University)
• Published : 2012.01.31

#### Abstract

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

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#### Cited by

1. Stochastic Processes and Spectral Analysis for Hilbert $$C^*$$ C ∗ -Module-Valued Maps 2015, https://doi.org/10.1007/s40840-015-0270-6
2. A Stinespring type theorem for completely positive multilinear maps on Hilbert -modules pp.1563-5139, 2017, https://doi.org/10.1080/03081087.2017.1411880