  Memory effects play a fundamental role in the study of the dynamics of open
quantum systems. There exist two conceptually distinct notions of memory
discussed for quantum channels in the literature. In quantum information theory
quantum channels with memory are characterised by the existence of correlations
between successive applications of the channel on a sequence of quantum
systems. In open quantum systems theory memory effects arise dynamically during
the time evolution of quantum systems, and define non-Markovian dynamics. Here
we relate and combine these two different concepts of memory. In particular, we
study the interplay between correlations between multiple uses of quantum
channels and non-Markovianity as non-divisibility of the $t$-parametrized
family of channels defining the dynamical map.
