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

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Springer Science & Business Media, Jan 15, 2011 - Science - 760 pages

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.

 

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Contents

Introduction
1
Algorithms and Computation
15
Basics of Classical Probability
29
Basics of InfiniteDimensional Analysis
36
Basics of Quantum Mechanics
61
Fundamentals of Classical Information Theory
101
Fundamentals of Quantum Information
124
Locality and Entanglement
167
Quantum Algorithms II
355
Quantum Algorithm III
369
Quantum Error Correction
397
Quantum Field Theory Locality and Entanglement
413
Quantum Cryptography
441
Quantum Teleportation
458
Physical Nanosystems
505
Miscellaneous in Quantum Theory and Information
521

Quantum Capacity and Coding
227
Information Dynamics and Adaptive Dynamics
251
Mathematical Models of Quantum Computer
313
Quantum Algorithms I
330
Applications to Life Science
607
References
719
Index
750
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About the author (2011)

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

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