A Preferred Definition of Conditional R´enyi Entropy

In this paper, we focus on the definitions of conditional R´enyi entropy, and select one of them on the basis of a relation between R´enyi and Tsallis entropies, and show that the chain rule holds generally for the case of conditional R´enyi entropy. Then, using this definition, we show some of the properties of conditional R´enyi entropy. Finally, we show the relations among R´enyi, Shannon and Tsallis entropies.