Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems (Theoretical and Mathematical Physics)

This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described. Front Matter....Pages I-XIX Introduction....Pages 1-13 Algorithms and Computation....Pages 15-28 Basics of Classical Probability....Pages 29-35 Basics of Infinite-Dimensional Analysis....Pages 37-59 Basics of Quantum Mechanics....Pages 61-100 Fundamentals of Classical Information Theory....Pages 101-123 Fundamentals of Quantum Information....Pages 125-166 Locality and Entanglement....Pages 167-225 Quantum Capacity and Coding....Pages 227-250 Information Dynamics and Adaptive Dynamics....Pages 251-312 Mathematical Models of Quantum Computer....Pages 313-329 Quantum Algorithms I....Pages 331-354 Quantum Algorithms II....Pages 355-368 Quantum Algorithm III....Pages 369-395 Quantum Error Correction....Pages 397-412 Quantum Field Theory, Locality and Entanglement....Pages 413-440 Quantum Cryptography....Pages 441-457 Quantum Teleportation....Pages 459-504 Physical Nanosystems....Pages 505-519 Miscellaneous in Quantum Theory and Information....Pages 521-606 Applications to Life Science....Pages 607-718 Back Matter....Pages 719-759 Introduction -- Algorithms And Computation -- Basics Of Classical Probability -- Basics Of Infinite-dimensional Analysis -- Basics Of Quantum Mechanics -- Fundamentals Of Classical Information Theory -- Fundamentals Of Quantum Information -- Locality And Entanglement -- Quantum Capacity And Coding -- Information Dynamics And Adaptive Dynamics -- Mathematical Models Of Quantum Computer -- Quantum Algorithms -- Quantum Error Correction -- Quantum Field Theory, Locality And Entanglement -- Quantum Cryptography -- Quantum Teleportation -- Physical Nanosystems -- Miscellaneous In Quantum Theory And Information -- Applications To Life Science. Masanori Ohya, Igor Volovich. Includes Bibliographical References (p. 719-749) And Index.