Bounding generalized relative entropies: Nonasymptotic quantum speed limits

Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language study variety of areas. Remarkably, one the key information-theoretic quantities is given by relative entropy, which quantifies how difficult tell apart two probability distributions, or even states. Such quantity rests at core fields like metrology, thermodynamics, communication, information. Given this broadness applications, desirable changes under process. By considering general unitary channel, we establish bound on generalized entropies (R\'enyi Tsallis) between output input channel. As application our bounds, derive family speed limits based entropies. Possible connections with coherence, asymmetry, single-shot information are briefly discussed.