Non-Markovianity of a Gaussian quantum Brownian motion channel using generalized LFS and Gaussian interferometric power measures

The non-monotonic behavior of the quantities such as Gaussian interferometric power and mutual information indicates the non-Markovianity of a dynamics through which two non-Markovianity measures have been introduced, Gaussian interferometric power measure for discrete and continuous variable systems and LFS measure for discrete variable systems. In this paper, we generalize the LFS measure to continuous variable systems. Then, we study and compare the degree of non-Markovianity of the continuous variable quantum Brownian motion channel using the above two measures. We consider an Ohmic environment with Lorentz-Drude cut-off and initial states, including the entangled thermal vacuum state and the separable mixed thermal state. It is observed that the degree of non-Markovianity depends on the parameters of the environment, the system and the applied measures. In addition, if thermal vacuum state is assumed as the initial state and the above measures have been used, the degree of non-Markovianity can be considered as that of the channel.