Abstract

In many fundamental problems of information theory and statistics, the efficiency of an asymptotically optimal protocol can be expressed by the relative entropy of certain states, or some derived quantity of it (entropy, conditional entropy, mutual information, etc.). In a more detailed analysis of these protocols, e.g., in the study of the exact decay rates of the relevant error probabilities, the efficiency is usually characterized by a Renyi relative entropy or a related quantity (like the Chernoff and the Hoeffding distances). In this talk I demonstrate the central importance of the Renyi relative entropies through a number of problems, including the discrimination of correlated quantum states, data compression, classical-quantum channel coding and the reversibility of quantum operations.