In central topic of the thesis is represented by the quantum correlations, such as entanglement, steering and discord, in continuous variable systems, described by Gaussian states.

We propose a novel method of entanglement detection in generic Gaussian states by using witnesses based on second moments, that compared to other methods requires on average fewer measurements than in full tomography, by which the whole state of the corresponding system is reconstructed. Furthermore, a similar approach is applied for detecting quantum steering in Gaussian states, where we define and fully characterise the set of steering witnesses based on second moments. In order to check the feasibility of this method we provide the simulation of entanglement and steering detection in random Gaussian states, showing a good robustness to statistical errors.

In the framework of the theory of open quantum systems based on completely positive dynamical semigroups, we solve the Lindblad master equation for a bipartite Gaussian system interacting with a thermal and a squeezed thermal reservoir. The overall evolution results as an effect of the competition between bath parameters, such as temperature and dissipation, and the characteristics of the initial state, such as squeezing and coupling between the modes of the considered system. Thus, for uncoupled modes entanglement and steering typically undergo a sudden suppression in finite times, whereas discord-type correlations vanish asymptotically for large times. However, if the modes are coupled, even the generation of Gaussian discord takes place for an initial state with only classical correlations, and it tends to a non-zero value in the asymptotic limit.

In addition, we study the evolution of the entropy production rate as a measure of irreversibility generated by the interaction of two bosonic modes with a thermal environment, which is always a positive quantity for the Markovian dynamics. Irreversibility is higher for any asymmetry in the system, such as squeezing and non-resonant frequencies, as well as in the case of coupled bosonic modes.