Abstract
In this paper, we continue the investigation of quantum Markov states (QMSs) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the most important open problems in quantum probability, which concerns the calculations of mean entropies of quantum Markov fields. Moreover, it opens up a new perspective for the generalization of many interesting results related to the one-dimensional QMSs and quantum Markov chains to multi-dimensional cases.