Dynamics of global entanglement under decoherence

We investigate the dynamics of global entanglement, the Meyer-Wallach measure, under decoherence, analytically. We study two important classes of multi-partite entangled states, the Greenberger-Horne-Zeilinger and the W state. We obtain exact results for various models of system-environment interactions (decoherence). Our results shows distinctly different scaling behavior for these initially entangled states indicating a relative robustness of the W state, consistent with previous studies.