A general theory of comparison of quantum channels (and beyond)

Anna Jenčová

Published 2020-02-11Version 1

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. These questions are studied in an extension of the framework of general probabilistic theories (GPT),suitable for dealing with channels. This extension carries a natural norm, which is an extension of the base norm and for quantum channels is the diamond norm. Using this norm, we introduce the notion of deficiency of one channel with respect to the other, defined as the accuracy of simulation by a given set of transformations. We prove a general randomization theorem in the GPT setting, giving an operational interpretation of the deficiency. This theorem is applied to some specific cases of simulability of quantum channels and measurements, obtaining a characterization of deficiency in terms of conditional min-entropies as well as success probabilities in guessing games.