The rise and fall of quantum and classical correlations in open-system dynamics

Coupling a set of initially uncorrelated subsystems leads to the generation of correlations. If in addition these subsystems interact with a dissipative local environments the generation of correlation can be restricted. It is found that the generation of quantum and classical correlations between the subsystems is qualitatively different in this respect. Quantum correlations (entanglement) display $k$-independent asymptotic behavior at large effective Hilbert space dimension $k$ of the composite system. As a consequence, the quantum correlations are bounded. Classical correlations are found numerically to develop on a scale growing with the effective Hilbert space dimension $k$ of the composite system. The rapid elimination of quantum correlations depends on the local environment. Such behavior is found for a singular bath of pure dephasing and for an energy dissipation bath. On the other hand, a Poissonian pure dephasing model does not lead to a rapid decay of quantum correlations. The phenomena are illustrated in a model of two coupled harmonic oscillators in interaction with different types of local environments