  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 the correlation between two quantum systems is
broken after a sufficiently long time passes. The first goal of this paper is
to show that asymptotic decoupling is equivalent to local mixing which asserts
the convergence to a unique stationary state on at least one quantum system. In
the study of Markovian dynamics, mixing and ergodicity are fundamental
properties which assert the convergence and the convergence of the long-time
average, respectively. The second goal of this paper is to show that mixing for
dynamics is equivalent to ergodicity for the two-fold tensor product of
dynamics. This equivalence gives us 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 (GPTs), but we also summarize them in quantum
theory.
