  We explore the possibility to generate nonlocal dynamical maps of an open
quantum system through local system-environment interactions. Employing a
generic decoherence process induced by a local interaction Hamiltonian, we show
that initial correlations in a composite environment can lead to a nonlocal
open system dynamics which exhibits strong memory effects although the local
dynamics is Markovian. In a model of two entangled photons interacting with two
dephasing environments we find a direct connection between the degree of memory
effects and the amount of correlations in the initial environmental state. The
results demonstrate that, contrary to conventional wisdom, enlarging an open
system can change the dynamics from Markovian to non-Markovian.
