Asymptotic properties for Markovian dynamics in quantum theory and general probabilistic theories

Abstract

We address asymptotic decoupling in the context of Markovian quantum dynamics. Asymptotic decoupling is an asymptotic property on a bipartite quantum system, and asserts that any correlation between two quantum systems is broken after a sufficiently long time passes. In this paper, we show that asymptotic decoupling is equivalent to local mixing which asserts the convergence to a unique stationary state on at least one quantum system. If dynamics is asymptotically decoupling, any correlation between two quantum systems is broken exponentially. Also, we give a criterion of mixing that is a system of linear equations. All results in this paper are proved in the framework of general probabilistic theories, but we also summarize them in quantum theory.