FREUDENBERG W. BRANDENBRUGISCHE TECH UNIV., MATH., PROF., 数学科, 教授
INOUE Kei SCIENCE UNIV.OF TOKYO,INFOR.SCIENCES,ASSISTANT, 理工学部, 助手 (70307700)
WATANABE Noboru SCIENCE UNIV.OF TOKYO,INFOR.SCIENCES,LECTURER, 理工学部, 講師 (70191781)
AKASHI Shigeo NIIGATA UNIV., MATH., ASSOCIATE PROF., 理学部, 助教授 (30202518)
OJIMA Izumi KYOTO UNIV., RIMS,ASSOCIATE PROF., 数理解析研究所, 助教授 (60150322)
The main purposes of our joint research program are to study several fields 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 :
 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 (Accardi, Akashi, Fichtner, Freudenberg, Kossakowski, Lu, Ohya, Ojima, Petz, Watanabe) studied the following topics of quantum information theory ; (1) channels, liftings, mathematical expression of beam splitting process, (2) pntical modulations, (3) amplification process, (4) multiple attenuation
process, (5) capacity of quantum ****nels
 Quantum Cornputer A fundamental object for quantum computation is the entangled state. Mathematicalconstruction and classificaton of the entangled states have been studied by Belavkin and Ohya. Ohya and Watanabe reformulated the FTM (Fredkin - Toffoli - Milburn) gate by means of quantum channeland rigorously proved the information conservation in the FTM gate. The mathematical construction of quantum logical gate was studied by [Ohya, Freudeberg, Watanabe] based on symmetric Fock spces. A nonlinear channel for a quantum teleportation process is rigorously constructed by [Accardi, Ohya, Inoue].
 Complexity : Ohya proposed a new theory of the complexity, ID, which has been applied to various studies such that (1) quantum communication, (2) analysis of genome sequences, (3) description of chaos, (4) dynamical entropy, (5) characterization of shapes, (6) economics, (7) recognition processes, etc. 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, Kossakowski, Inoue, Matsuoka] have studied several fields using these new measures.
 Information Genetics : Genome sequences are considered to carry information, and the information is storedin genome or amino acid sequences so that it originates the life itself. Ohya discussed how information theory is used to investigate the "information" stored in DNA.In particular, he introduced the concept of entropy evolution rate to classify the species and the algorithm for the use of coding theory to study the evolution of species. We [Ohya, Satoul analyze the condition of patients contracted HIV by mean of the entropy evolution rate and the chaos degree. Less