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

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.