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

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. Shor's 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. Boltzmann's entropy; Appendix B. Shannon's 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 Shor's algorithm; Appendix T. Modular arithmetic and Euler's Theorem; Appendix U. Klein's 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.