Renyi-Holevo Inequality from α- z -Renyi Relative Entropies

Abstract

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the α-z-R´enyi relative entropies, which comprise known relevant quantities such as the R´enyi relative entropy and the sandwiched R´enyi relative entropy, we establish the Holevo-R´enyi inequality. This result leads to a quantum bound for the α-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.