  Markov states have been defined for tripartite quantum systems. In this
paper, we generalize the definition of the Markov states to arbitrary
multipartite case and find the general structure of an important subset of
them, which we will call strong Markov states. In addition, we focus on an
important property of the Markov states: If the initial state of the whole
system-environment is a Markov state, then each localized dynamics of the whole
system-environment reduces to a localized subdynamics of the 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 Markov state. 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.
