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.

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 Jakobczyk, Mathematical Reviews, Issue 2012 c)

• 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.