Dynamics of non-classically-reproducible entanglement

We investigate when the quantum correlations of a bipartite system, under the influence of environments with memory, are not reproducible with certainty by a classical local hidden variable model. For this purpose, we compare the dynamics of a Bell inequality with that of entanglement, as measured by concurrence. We find time regions when the Bell inequality is not violated even in correspondence with high values of concurrence (up to approximate to 0.8). We also suggest that these results may be observed by adopting a modification of a recent experimental optical setup. These findings indicate that even highly entangled systems cannot be exploited with certainty in contexts where the nonclassical reproducibility of quantum correlations is required.