Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems

Providing an introduction to mathematical aspects of quantum information and open systems, this volume provides a unique combination of applications to bio- and nano-systems. Readers will find a new paradigm for quantum computation, as well as introductory treatment of functional analysis.

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.

A unique combination of rigorous mathematical results in quantum information and applications to nano-systems and life science Presents a new paradigm for quantum computation beyond the usual quantum Turing machine With introductory material to mathematics and quantum theory Includes supplementary material: sn.pub/extras

Auteur
M. Ohya (Tokyo University of Science) and I. Volovich (SMI RAS, Russia) are acknowledged experts on quantum information theory.

Contenu
1 Introduction.- 2 Algorithms and Computation.- 3 Basics of Classical Probability.- 4 Basics of Infinite Dimensional Analysis.- 5 Basics of Quantum Mechanics.- 6 Fundamentals of Classical Information Theory.- 7 Fundamentals of Quantum Information.- 8 Locality and Entanglement.- 9 Quantum Capacity and Coding.- 10 Information Dynamics and Adaptive Dynamics.- 11 Mathematical Models of Quantum Computer.- 12 Quantum Algorithms I.- 13 Quantum Algorithms II.- 14 Quantum Algorithms III.- 15 Quantum Error Correction.- 16 Quantum Field Theory.- Locality and Entanglement.- 17 Quantum Cryptography.- 18 Quantum Teleportation.- 19 Physical Nano-Systems.- 20 Miscellaneous in Quantum Theory and Information.- 21 Applications to Life Science.