Non-divisibility vs backflow of information in understanding revivals of quantum correlations for continuous-variable systems interacting with fluctuating environments

We address the dynamics of quantum correlations for a bipartite continuous-variable quantum system interacting with its fluctuating environment. In particular, we consider two independent quantum oscillators initially prepared in a Gaussian state, e.g. a squeezed thermal state, and compare the dynamics resulting from local noise, i.e. oscillators coupled to two independent external fields, to that originating from common noise, i.e. oscillators interacting with a single common field. We prove non-Markovianity (non-divisibility) of the dynamics in both regimes and analyze the connections between non-divisibility, backflow of information and revivals of quantum correlations. Our main results may be summarized as follows: (i) revivals of quantumness are present in both scenarios, however, the interaction with a common environment better preserves the quantum features of the system; (ii) the dynamics is always non-divisible but revivals of quantum correlations are present only when backflow of information is present as well. We conclude that non-divisibility in its own is not a resource to preserve quantum correlations in our system, i.e. it is not sufficient to observe recoherence phenomena. Rather, it represents a necessary prerequisite to obtain backflow of information, which is the true ingredient to obtain revivals of quantumness.