Tight Contraction Rates for Primitive Channels under Quantum $f$-Divergences

Researchers have made significant progress in understanding the behavior of quantum channels under various measures of distinguishability, particularly quantum $f$-divergences. The strong data-processing inequality (SDPI) constants, which quantify the degree to which two probability distributions become less distinguishable under a given channel, have been found to have tight contraction rates for primitive channels. This advancement has important implications for the field of quantum information processing, as it provides a finer-grained understanding of how quantum channels affect the distinguishability of probability distributions. The results are based on a rigorous analysis of the contraction rates of quantum $f$-divergences under primitive channels, and have been shown to be tight, meaning that they cannot be improved upon¹. This matters to quantum information processing practitioners because it provides a more accurate understanding of how quantum channels behave, allowing for more informed decisions about quantum system design and security.