On Quantum Entropies for the Compound Quantum Channel

In classical information theory, the most important theorems are the cod-ing theorems, which were discussed by calculating the mean entropy and the mean mu-tual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quan-tum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. Afterthat, several approaches for introducing the quantum dynamical entropy were proposed[10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for thequantum processes is investigated by using the von Neumann entropy [22] and the Ohyamutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26, 27] ingeneral quantum systems. The mean entropy and the mean mutual entropy for the quantumdynamical systems were introduced based on the S-mixing entropy. In this paper, basedon research into the dynamical entropy and mean mutual entropy of quantum systems,this study investigates the characteristics of quantum channels that exhibit entanglement,a property unique to quantum systems, and investigates the behaviour of quantum entropyfor compound quantum channels by changing the perspective from information transmis-sion between input and output to a new perspective of information transmission from theinitial state to the final state.