Discord and decoherence

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of "quantum correlations"between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties.