We analyze the evolution of the Gaussian discord between two resonant harmonic oscillators coupled to a common environment. For this, we use the same tools we applied before to fully characterize the evolution of the entanglement in this system [Paz and Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. The asymptotic value of Gaussian discord is obtained as a function of parameters characterizing the environment (temperature, couplings, etc.) and the initial state of the system (initial squeezing, initial purity, etc.) The type of Gaussian measurement optimizing the extraction of information between the oscillators is fully characterized by means of a phase diagram. Such a diagram (with phases corresponding to homodyne or heterodyne measurements) has similar topology to the one describing dynamical phases for the entanglement. We present evidence pointing to the fact that Gaussian discord is not always a good approximation of true discord as the asymptotic value of the former is shown to be a nondecreasing function of temperature (in the high-temperature regime), reaching an asymptotic value of $\ln \left(2\right)$ for a pure initial state (and lower values for mixed initial states).

• Received 14 November 2011

DOI:https://doi.org/10.1103/PhysRevA.85.032118