  Process tensors are quantum combs describing the evolution of open quantum
systems through multiple steps of a quantum dynamics. While there is more than
one way to measure how different two processes are, special care must be taken
to ensure quantifiers obey physically desirable conditions such as data
processing inequalities. Here, we analyze two classes of distinguishability
measures commonly used in general applications of quantum combs. We show that
the first class, called Choi divergences, does not satisfy an important data
processing inequality, while the second one, which we call generalized
divergences, does. We also extend to quantum combs some other relevant results
of generalized divergences of quantum channels. Finally, given the properties
we proved, we argue that generalized divergences may be more adequate than Choi
divergences for distinguishing quantum combs in most of their applications.
Particularly, this is crucial for defining monotones for resource theories
whose states have a comb structure, such as resource theories of quantum
processes and resource theories of quantum strategies.
