Renyi Entropy and Renyi Divergence in Sequential Effect Algebra

摘要

The aim of this study is to extend the results concerning the Shannon entropy and Kullback-Leibler divergence in sequential effect algebra to the case of Renyi entropy and Renyi divergence. For this purpose, the Renyi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Renyi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback-Leibler divergence and Shannon's entropy of partitions in a given sequential effect algebra can be obtained as limits of their Renyi divergence and Renyi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.