Geometric versus Entropic Gaussian Correlations in an Open Quantum System of Two Bosonic Modes

Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification of total nonclassical correlations of Gaussian states. We consider the special case when the initial squeezed thermal state of the system preserves its form in time. We show that time evolution of the measures strongly depends on the parameters characterising the initial state of the system (squeezing parameter and average thermal photon numbers of the two modes) and of the thermal environment (temperature of the thermal bath and dissipation rate). In the limit of large times all the considered measures asymptotically tend to zero value, corresponding to an asymptotic bimodal uncorrelated product state. We make a comparison between the behaviour of the evolution in time of the Gaussian geometric quantum correlations and Gaussian entropic quantum correlations.