Markov states have been defined for tripartite quantum systems. In thispaper, we generalize the definition of the Markov states to arbitrarymultipartite case and find the general structure of an important subset ofthem, which we will call strong Markov (SM) states.. In addition, we focus onan important property of the Markov states: If the initial state of the wholesystem-environment is a Markov state, then each localized dynamics of the wholesystem-environment reduces to a localized subdynamics of the system. Thisprovides us a necessary condition for entanglement revival in an open quantumsystem: Entanglement revival can occur only when the system-environment stateis not a Markov state. To illustrate (a part of) our results, we consider thecase that the environment is modeled as classical. In this case, though thecorrelation between the system and the environment remains classical during theevolution, the change of the state of the system-environment, from its initialMarkov state to a state which is not a Markov one, leads to the entanglementrevival in the system. This shows that the non-Makovianity of a state is notequivalent to the existence of non-classical correlation in it, in general.
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