  We introduce a non-Markovianity measure for continuous variable open quantum
systems based on the idea put forward in H.-P. Breuer et al., Phys. Rev.
Lett.\textbf{103}, 210401 (2009), i.e., by quantifying the flow of information
from the environment back to the open system. Instead of the trace distance we
use here the fidelity to assess distinguishability of quantum states. We employ
our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels:
the purely damping channel and the quantum Brownian motion channel with Ohmic
environment. We consider different classes of Gaussian states and look for
pairs of states maximizing the backflow of information. For coherent states we
find simple analytical solutions, whereas for squeezed states we provide both
exact numerical and approximate analytical solutions in the weak coupling
limit.
