Unifying Entropies of Quantum Logic Based on Rényi Entropies

The aim of this study it to unify entropies of quantum logic. For this purpose, Rényi entropy of partition of quantum logic corresponding to a state is presented and formal properties of a proper definition of an entropy are detected. In addition, an appropriate definition of conditional Rényi entropy of quantum logic having the expected properties such as monotonicity is proposed. Finally, Rényi entropy of quantum dynamical system is mentioned and it is proved that it is invariant under isomorphism.