Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems / Edition 1

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Overview

This monograph provides an introduction to the mathematical aspects of the theory of quantum information and open systems, with applications to various nano and bio systems.

It includes introductory material on functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information, the authors discuss findings on quantum mutual entropy, 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, 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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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9789400701700
  • Publisher: Springer Netherlands
  • Publication date: 1/7/2011
  • Series: Theoretical and Mathematical Physics Series
  • Edition description: 2011
  • Edition number: 1
  • Pages: 760
  • Product dimensions: 6.10 (w) x 9.20 (h) x 1.80 (d)

Meet the Author

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

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Table of Contents

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.

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