Role of entanglement for nonlocal memory effects

We determine the role of entanglement for nonlocal memory effects induced by initial correlations in a composite environment. The dephasing dynamics of two two-level systems which are coupled locally to an environment consisting of nonlocally correlated field modes is studied with respect to the occurrence of reviving nonlocal coherences. Employing two-mode Gaussian states correlating pairs of modes of the bosonic baths we observe strong nonlocal memory effects in this locally Markovian dynamics for entangled as well as separable quantum states for the environment. We present an explanation for this phenomenon linking it to the correlation coefficient of the environmental coupling operators and derive a necessary and sufficient condition for the occurrence of nonlocal memory effects for sufficiently short interaction times. Finally, we comment on how the magnitude of the nonlocal rephasing may also be used to estimate parameters of the two-mode Gaussian states.