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We consider two qubits interacting with a common bosonic bath, but notdirectly between themselves. We derive the (bipartite) entanglement generationconditions for Gaussian non-Markovian dynamical maps and show that they aresimilar as in the Markovian regime; however, they depend on different physicalcoefficients and hold on different time scales. Indeed, for small times, in thenon-Markovian regime entanglement is possibly generated on a shorter time scale($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although thesingular coupling limit of non-Markovian dynamics yields Markovian ones, weshow that the same limit does not lead from non-Markovian entanglementgeneration conditions to Markovian ones. Also, the entanglement generationconditions do not depend on the initial time for non-Markovian open dynamicsresulting from couplings to bosonic Gaussian baths, while they may depend ontime for open dynamics originated by couplings to classical, stochasticGaussian environments.

Qubit Entanglement generation by Gaussian non-Markovian dynamics