  We present a general theory of comparison of quantum channels, concerning
with the question of simulability or approximate simulability of a given
quantum channel by allowed transformations of another given channel. We
introduce a modification of conditional min-entropies, with respect to the set
F of allowed transformations, and show that under some conditions on F, these
quantities characterize approximate simulability. If F is the set of free
superchannels in a quantum resource theory of processes, the modified
conditional min-entropies form a complete set of resource monotones. If the
transformations in F consist of a preprocessing and a postprocessing of
specified forms, approximate simulability is also characterized in terms of
success probabilities in certain guessing games, where a preprocessing of a
given form can be chosen and the measurements are restricted. These results are
applied to several specific cases of simulability of quantum channels,
including postprocessings, preprocessings and processing of bipartite channels
by LOCC superchannels and by partial superchannels, as well as simulability of
sets of quantum measurements.
  These questions are first studied in a general setting that is an extension
of the framework of general probabilistic theories (GPT), suitable for dealing
with channels. Here we prove a general theorem that shows that approximate
simulability can be characterized by comparing outcome probabilities in certain
tests. This result is inspired by the classical Le Cam randomization criterion
for statistical experiments and contains its finite dimensional version as a
special case.
