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The concept of divisibility of dynamical maps is used to introduce ananalogous concept for quantum channels by analyzing the \textit{simulability}of channels by means of dynamical maps. In particular, this is addressed forLindblad divisible, completely positive divisible and positive divisibledynamical maps. The corresponding L-divisible, CP-divisible and P-divisiblesubsets 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 qubitchannels. We discuss the general inclusions among divisibility sets and showseveral equivalences for qubit channels. To this end we study the conditions ofL-divisibility for finite dimensional channels, especially the cases withnegative eigenvalues, extending and completing the results of Phys. Rev. Lett.,101(15):150402, 2008. Furthermore we show that transitions between every two ofthe defined divisibility sets are allowed. We explore particular examples ofdynamical maps to compare these concepts. Finally, we show that every divisiblebut not infinitesimal divisible qubit channel (in positive maps) isentanglement breaking, and open the question if something similar occurs forhigher dimensions.

Divisibility of qubit channels and dynamical maps