INFORMATION DYNAMICAL STUDY OF OPTICAL COMMUNICATION THEORY

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The main purpose of our joint research program is to study optical communication theoty based on Information Dynamics (ID for short). The concept of ID is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems altogether. We have studied the following topics during the period of the joint research program :[1] Quantum Information : Quantum information theory has been developed from entropy theory and quantum statistics, and several concepts such as quantum mutual entropy and capacity in this theory play fundamental roles in recent development of optical communication and quantum computer. Furthermore, we (Ohya, Suyari, Watanabe) studied the following topics of quantum information Theory ; (1) channels, liftings, mathematical expression of beam splitting process, (2) optical modulations, (3) amplification process, (4) multiple attenuation p**cess, (5) capacity of quantum channels.[2] Quant … More um Computer : A fundamental object for quantum computation is the entangled state. Mathematical construction and classificaton of the entangled states have been studied by Belavkin and Ohya. Ohya and Watanabe reformulated the FTM (Fredkin - Toffoli - Milbum) gate by means of quantum channel and rigorously proved the information conservation in the FTM gate. The mathematical construction of quantum logical gate was studied by [Ohya, Watanabe] based on symmetric Fock spces. A nonlinear channel for a quantum teleportation process is rigorously constructed by [Ohya, Suyari, Inoue].[3] Complexity : Ohya proposed a new theory of the complexity, ID, which has been applied to various studies such that (1) quantum communication, (3) description of chaos, (4) dynamical entropy, (5) characterization of shapes. In particular, in the framework of ID, new measures for complex system, that is, the fractal dimensions for states and the chaos degree have been introduced, which enabled us to characterize chaotic aspects of the dynamics associated to several systems. We [Ohya, Inoue, Matsuoka] have studied several fields using these new measures. Less