Classical and Quantum Information Theory: An Introduction for the Telecom Scientist

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Cambridge University Press, Feb 19, 2009 - Technology & Engineering
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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.
 

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Contents

1 Probability basics
1
2 Probability distributions
20
3 Measuring information
37
4 Entropy
50
5 Mutual information and more entropies
69
6 Differential entropy
84
7 Algorithmic entropy and Kolmogorov complexity
96
8 Information coding
127
Appendix B Chapter 4 Shannons entropy1
568
Appendix C Chapter 4 Maximum entropy of discrete sources
573
Appendix D Chapter 5 Markov chains and the second law of thermodynamics
581
Appendix E Chapter 6 From discrete to continuous entropy
587
Appendix F Chapter 8 KraftMcMillan inequality
589
Appendix G Chapter 9 Overview of data compression standards
591
Appendix H Chapter 10 Arithmetic coding algorithm
605
Appendix I Chapter 10 LempelZiv distinct parsing
610

9 Optimal coding and compression
151
10 Integer arithmetic and adaptive coding
179
11 Error correction
208
12 Channel entropy
232
13 Channel capacity and coding theorem
245
14 Gaussian channel and ShannonHartley theorem
264
15 Reversible computation
283
16 Quantum bits and quantum gates
304
17 Quantum measurements
333
18 Qubit measurements superdense coding and quantum teleportation
356
19 DeutschJozsa quantum Fourier transform and Grover quantum database search algorithms
378
20 Shors factorization algorithm
399
21 Quantum information theory
431
22 Quantum data compression
457
23 Quantum channel noise and channel capacity
475
24 Quantum error correction
496
25 Classical and quantum cryptography
523
Appendix A Chapter 4 Boltzmanns entropy
565
Appendix J Chapter 11 Errorcorrection capability of linear block codes
614
Appendix K Chapter 13 Capacity of binary communication channels
617
Appendix L Chapter 13 Converse proof of the channel coding theorem
621
Appendix M Chapter 16 Bloch sphere representation of the qubit
625
Appendix N Chapter 16 Pauli matrices rotations and unitary operators
627
Appendix O Chapter 17 Heisenberg uncertainty principle
635
Appendix P Chapter 18 Twoqubit teleportation
637
Appendix Q Chapter 19 Quantum Fourier transform circuit
644
Appendix R Chapter 20 Properties of continued fraction expansion
648
Appendix S Chapter 20 Computation of inverse Fourier transform in the factorization of through Shors algorithm
653
Appendix T Chapter 20 Modular arithmetic and Eulers theorem
656
Appendix U Chapter 21 Kleins inequality
660
Appendix V Chapter 21 Schmidt decomposition of joint pure states
662
Appendix W Chapter 21 State purification
664
Appendix X Chapter 21 Holevo bound
666
Appendix Y Chapter 25 Polynomial byte representation and modular multiplication
672
Index
676
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About the author (2009)

Emmanuel Desurvire is Director of the Physics Research Group at Thales Research and Technology, and has held previous positions at Stanford University, AT&T Bell Laboratories, Columbia University and Alcatel. With over 25 years' experience in the field of optical communications, he has received numerous recognitions for his scientific contributions, including the 1998 Benjamin Franklin Medal in Engineering, the 2005 William Streifer Scientific Achievement Award, and, in 2007, the IEEE/LEOS John Tyndall Award, Engineer of the Year Award and the France-Telecom Prize of the Académie des Sciences.

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