A Note on Complexities by Means of Quantum Compound Systems

Abstract

It has been shown that joint probability distributions of quantum systems generally do not exist, and the key to solving this concern is the compound state invented by Ohya. The Ohya compound state constructed by the Schatten decomposition (i.e., one-dimensional orthogonal projection) of the input state shows the correlation between the states of the input and output systems. In 1983, Ohya formulated the quantum mutual entropy by applying this compound state. Since this mutual entropy satisfies the fundamental inequality, one may say that it represents the amount of information correctly transmitted from the input system through the channel to the output system, and it may play an important role in discussing the efficiency of information transfer in quantum systems. Since the Ohya compound state is separable state, it is important that we must look more carefully into the entangled compound state.

Keywords

• quantum entropy
• quantum information
• quantum compound system