  Quantum information processing and computing tasks can be understood as
quantum networks, comprising quantum states and channels and possible physical
transformations on them. It is hence pertinent to estimate the change in
informational content of quantum processes due to physical transformations they
undergo. The physical transformations of quantum states are described by
quantum channels, while the transformations of quantum channels are described
by quantum superchannels. In this work, we determine fundamental limitations on
how well the physical transformation on quantum channels can be undone or
reversed, which are of crucial interest to design and benchmark quantum
information and computation devices. In particular, we refine (strengthen) the
quantum data processing inequality for quantum channels under the action of
quantum superchannels. We identify a class of quantum superchannels, which
appears to be the superchannel analogue of subunital quantum channels, under
the action of which the entropy of an arbitrary quantum channel is
nondecreasing. We also provide a refined inequality for the entropy change of
quantum channels under the action of an arbitrary quantum superchannel.
