Classical and Quantum Information Theory

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.

Spis treści:
1. Probabilities 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 measurments
18. Qubit measurements, superdense coding and quantum teleportation
19. Deutsch/Jozsa alorithms and quantum fourier transform
20. Shors factorization algorithm
21. Quantum information theory
22. Quantum compression
23. Quantum channel noise and channel capacity
24. Quantum error correction
25. Classical and quantum cryptography
Appendix A. Boltzmanns entropy
Appendix B. Shannons entropy
Appendix C. Maximum entropy of discrete sources
Appendix D. Markov chains and the second law of thermodynamics
Appendix E. From discrete to continuous entropy
Appendix F. Kraft-McMillan inequality
Appendix G. Overview of data compression standards
Appendix H. Arithmetic coding algorithm
Appendix I. Lempel-Ziv distinct parsing
Appendix J. Error-correction capability of linear block codes
Appendix K. Capacity of binary communication channels
Appendix L. Converse proof of the Channel Coding Theorem
Appendix M. Block sphere representation of the qubit
Appendix N. Pauli matrices, rotations and unitary operators
Appendix O. Heisenberg Uncertainty Principle
Appendix P. Two qubit teleportation
Appendix Q. Quantum Fourier transform circuit
Appendix R. Properties of continued fraction expansion
Appendix S. Computation of inverse Fourier transform in the factoring of N=21 through Shors algorithm
Appendix T. Modular arithmetic and Eulers Theorem
Appendix U. Kleins inequality
Appendix V. Schmidt decomposition of joint pure states
Appendix W. State purification
Appendix X. Holevo bound
Appendix Y. Polynomial byte representation and modular multiplication.