Fundamental limitations on the recoverability of quantum processes

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 can the physical transformation on quantum channels be undone or reversed, which are of crucial interest to design and benchmark quantum information and computation devices. In particular, we refine the quantum data processing inequality for quantum channels by strengthening the monotonicity inequality of quantum relative entropy of quantum channels under the action of an arbitrary quantum superchannel. We identify a class of quantum superchannels, which appears to be quantum superchannel analogue of quantum subunital channels, under the action of which the entropy of an arbitrary quantum channel is nondecreasing.