Entropy Type Complexities In Quantum Dyn Amical Processes

In a study of several systems, we are interested to examine (1) the dynamics of state change and (2) the complexity of states. Ohya introduced in 1991 (ref.[21]) a general idea so-called a Information Dynamics (ID), which constitutes a theory under a frame of the ID by synthesizing the formalities of the investigations of (1) and (2). There are two kind of complexities in ID. One is a complexity of state describing system itself and another is a transmitted complexity between two systems. Entropies of classical and quantum systems are the example of these complexities. In order to treat a flow of dynamics process, dynamical entropies were introduced in not only classical but also quantum systems. The main purpose of this paper is to compare with these mean entropies and the complexities in rD, we calculate these mean entropies for some simple models to discuss the complexity of information transmission for OOK and PSK modulations.