  The concept of divisibility of dynamical maps is used to introduce an
analogous concept for quantum channels by analyzing the \textit{simulability}
of channels by means of dynamical maps. In particular, this is addressed for
Lindblad divisible, completely positive divisible and positive divisible
dynamical maps. The corresponding L-divisible, CP-divisible and P-divisible
subsets of channels are characterized (exploiting the results by Wolf et al.,
Comm. Math. Phys., 279(1):147-168, 2008) and visualized for the case of qubit
channels. We discuss the general inclusions among divisibility sets and show
several equivalences for qubit channels. To this end we study the conditions of
L-divisibility for finite dimensional channels, especially the cases with
negative eigenvalues, extending and completing the results of Phys. Rev. Lett.,
101(15):150402, 2008. Furthermore we show that transitions between every two of
the defined divisibility sets are allowed. We explore particular examples of
dynamical maps to compare these concepts. Finally, we show that every divisible
but not infinitesimal divisible qubit channel (in positive maps) is
entanglement breaking, and open the question if something similar occurs for
higher dimensions.
