α-z-Renyi relative entropy related quantities and their preservers

Various quantum relative entropies play important roles in classical and quantum information theory. In this paper, we generalize the definition of alpha-z-Renyi relative entropy from finite-dimensional quantum systems to infinite-dimensional quantum systems, give its some properties, and then determine the structure of all maps preserving alpha- z-Renyi relative entropy on positive trace-class operators. In addition, we also study alpha-z-Bures-Wasserstein divergences based on alpha-z-ernyi relative entropy on all positive trace-class operators, and give a complete characterization of all maps preserving alpha-z-Bures-Wasserstein divergences on the set of all positive trace-class operators and on the set of all positive invertible elements in a general C-*-algebra with a faithful finite trace, respectively.