Citation: Linden, Noah, Milan Mosonyi, and Andreas Winter. "The structure of Renyi entropic inequalities." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469.2158 (2013): 20120737.
Web: https://arxiv.org/abs/1212.0248
Tags: Information-theory
This paper proves a fantastic result - the Renyi entropy is NOT strongly subadditive for any alpha away from 1. Moreover, this paper proves that the Renyi entropy does not satisfy any other homogenous inequalities. It's not just that Renyi entropy satisfies a different similar looking inequality - Renyi entropy behaves truly differently than von Neumann entropy in this case. This can be seen as one of the major motivations for working with von Neumann entropy instead of Renyi entropy.
This paper is a good place to go to learn about, well, the structure of Renyi entropic inequalities.