Table of Contents

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.