  We analyze the steady state entanglement generated in a coherently coupled
dimer system subject to dephasing noise as a function of the degree of
Markovianity of the evolution. By keeping fixed the effective noise strength
while varying the memory time of the environment, we demonstrate that
non-Markovianity is an essential, quantifiable resource that may support the
formation of steady state entanglement whereas purely Markovian dynamics
governed by Lindblad master equations lead to separable steady states. This
result illustrates possible mechanisms leading to long-lived entanglement in
purely decohering, possibly local, environments. We present a feasible
experimental demonstration of this noise assisted phenomenon using a system of
trapped ions.
