  Quantum channels, pivotal in information processing, describe transformations
within quantum systems and enable secure communication and error correction.
Ergodic and mixing properties elucidate their behavior. In this paper, we
establish a sufficient condition for mixing based on a quantum Markov-Dobrushin
inequality. We prove that if the Markov-Dobrushin constant of a quantum channel
exceeds zero, it exhibits exponential mixing behavior. We explore limitations
of some quantum channels, demonstrating that unistochastic channels are not
mixing. Additionally, we analyze ergodicity of a class of mixed-unitary
channels associated with finite groups of unitary operators. Finally, we apply
our results to the qubit depolarizing channel.
