Collective dynamics of N -partite quantum systems: The role of entanglement, classical correlations, and interaction

Abstract

Entanglement between two noninteracting particles can give rise to their joint motion. This suggests that entanglement may be a kind of resource to activate collective behavior in multipartite systems. However, here we argue that entanglement is neither a necessary nor a sufficient condition for a multipartite collective dynamics. We consider an $N$-partite scenario and show that a genuinely multipartite entangled noninteracting system can move collectively. Nevertheless, at the same time any $M$-partite ($1<M<N$) subsystem, which also moves collectively, is classically correlated. Moreover, since there is no interaction, such a subsystem would behave the same way if the remaining $N\ensuremath{-}M$ particles were removed. This proves that entanglement is not necessary for a collective motion. Next, we introduce external potentials and show that some collective dynamical properties cannot be observed unless an interaction between the particles is turned on.