  We study the open dynamics of a quantum two-level system coupled to an
environment modeled by random matrices. Using the quantum channel formalism, we
investigate different quantum Markovianity measures and criteria. A thorough
analysis of the whole parameter space, reveals a wide range of different
regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast
to analytical models, all non-Markovianity measures and criteria have to be
applied to data with fluctuations and statistical uncertainties. We discuss the
practical usefulness of the different approaches.
