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

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

• 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.

From the reviews:“The monograph under review concerns a mathematically rigorous approach to quantum information and computation. The authors provide necessary introductory material on functional analysis, probability theory, information theory and quantum mechanics. … The unique feature of the monograph is that the authors also describe the applications of information theory to genetics and other life sciences. … Very helpful for further study is the vast list of references, containing the most important articles and books on the subject.” (Lech Jakóbczyk, Mathematical Reviews, Issue 2012 c)