Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case andfindthegeneralstructure of an important subset of them, which wewillcall strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the wholesystem–environmentisaMarkovstate,theneachlocalized dynamicsofthewholesystem–environmentreducestoalocalized subdynamics ofthe system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system–environment state is not a Markovstate. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system–environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.

Keywords