  We put forward a measure based on Gaussian steering to quantify the
non-Markovianity of continuous-variable (CV) Gaussian quantum channels. We
employ the proposed measure to assess and compare the non-Markovianity of a
quantum Brownian motion (QBM) channel, originating from the interaction with
Ohmic and sub-Ohmic environments with spectral densities described by a
Lorentz-Drude cutoff, both at high and low temperatures, showing that
sub-Ohmic, high temperature environments lead to highly non-Markovian
evolution, with cyclic backflows of Gaussian steerability from the environment
to the system. Our results add to the understanding of the interplay between
quantum correlations and non-Markovianity for CV systems, and could be
implemented at the experimental level to quantify non-Markovianity in some
physical scenarios.
