Classical and Quantum Information Theory

An Introduction for the Telecom Scientist

Emmanuel Desurvire

• Publisher: Cambridge University Press
• Year: 2009
• Print ISBN: 9780521881715
• eBook ISBN: 9780511501081
• Topic: Technology & Engineering
• Subtopic: Signals & Signal Processing
• Index: Technology & Engineering

Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Opening chapters present the basic concepts and various applications of Shannon's entropy, moving on to the core features of quantum information and quantum computing. Topics such as coding, compression, error-correction, cryptography and channel capacity are covered from classical and quantum viewpoints. Employing an informal yet scientifically accurate approach, Desurvire provides the reader with the knowledge to understand quantum gates and circuits. Highly illustrated, with numerous practical examples and end-of-chapter exercises, this text is ideal for graduate students and researchers in electrical engineering and computer science, and practitioners in the telecommunications industry. Further resources and instructor-only solutions are available at www.cambridge.org/9780521881715.

Table of contents

• Cover
• Half-title
• Title
• Copyright
• Contents
• Foreword
• Introduction
• Acknowledgments
• 1 Probability basics
• 2 Probability distributions
• 3 Measuring information
• 4 Entropy
• 5 Mutual information and more entropies
• 6 Differential entropy
• 7 Algorithmic entropy and Kolmogorov complexity
• 8 Information coding
• 9 Optimal coding and compression
• 10 Integer, arithmetic, and adaptive coding
• 11 Error correction
• 12 Channel entropy
• 13 Channel capacity and coding theorem
• 14 Gaussian channel and Shannon–Hartley theorem
• 15 Reversible computation
• 16 Quantum bits and quantum gates
• 17 Quantum measurements
• 18 Qubit measurements, superdense coding, and quantum teleportation
• 19 Deutsch–Jozsa, quantum Fourier transform, and Grover quantum database search algorithms
• 20 Shor's factorization algorithm
• 21 Quantum information theory
• 22 Quantum data compression
• 23 Quantum channel noise and channel capacity
• 24 Quantum error correction
• 25 Classical and quantum cryptography
• Appendix A (Chapter 4) Boltzmann's entropy
• Appendix B (Chapter 4) Shannon's entropy
• Appendix C (Chapter 4) Maximum entropy of discrete sources
• Appendix D (Chapter 5) Markov chains and the second law of thermodynamics
• Appendix E (Chapter 6) From discrete to continuous entropy
• Appendix F (Chapter 8) Kraft–McMillan inequality
• Appendix G (Chapter 9) Overview of data compression standards
• Appendix H (Chapter 10) Arithmetic coding algorithm
• Appendix I (Chapter 10) Lempel–Ziv distinct parsing
• Appendix J (Chapter 11) Error-correction capability of linear block codes
• Appendix K (Chapter 13) Capacity of binary communication channels
• Appendix L (Chapter 13) Converse proof of the channel coding theorem
• Appendix M (Chapter 16) Bloch sphere representation of the qubit
• Appendix N (Chapter 16) Pauli matrices, rotations, and unitary operators
• Appendix O (Chapter 17) Heisenberg uncertainty principle
• Appendix P (Chapter 18) Two-qubit teleportation
• Appendix Q (Chapter 19) Quantum Fourier transform circuit
• Appendix R (Chapter 20) Properties of continued fraction expansion
• Appendix S (Chapter 20) Computation of inverse Fourier transform in the factorization of N = 21 through Shor's algorithm
• Appendix T (Chapter 20) Modular arithmetic and Euler's theorem
• Appendix U (Chapter 21) Klein's inequality
• Appendix V (Chapter 21) Schmidt decomposition of joint pure states
• Appendix W (Chapter 21) State purification
• Appendix X (Chapter 21) Holevo bound
• Appendix Y (Chapter 25) Polynomial byte representation and modular multiplication
• Index