ASYMPTOTIC QUANTUM CORRELATIONS IN OPEN QUANTUM SYSTEMS

We describe the asymptotic behaviour of quantum correlations (quantum entanglement, quantum discord, and quantum steering) in a system composed of two coupled bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems. The time evolution of quantum correlations is described in terms of the covariance matrix for Gaussian initial states. We show that, depending on the values of the strength of interaction between the two bosonic modes, and independent of the initial state, in the limit of infinite time the system evolves asymptotically to an equilibrium state, which may be entangled or separable. We show also that for all non-zero values of the strength of interaction between the modes, Gaussian quantum discord tends asymptotically for large times to some definite non-zero value. The asymptotic values of entanglement and discord depend on the strength of interaction between the bosonic modes, temperature, and dissipation parameter. We calculate also the Gaussian quantum steering and find out that in the limit of large times it is zero for all values of the strength of interaction between the two modes.