Quantum Information Theory

Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject 'from the ground up' it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quantum information theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo information, and the superactivation of quantum capacity. This book will be warmly welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.How to use this book; Acknowledgements; Part I. Introduction: 1. Concepts in quantum Shannon theory; 2. Classical Shannon theory; Part II. The Quantum Theory: 3. The noiseless quantum theory; 4. The noisy quantum theory; 5. The purified quantum theory; Part III. Unit Quantum Protocols: 6. Three unit quantum protocols; 7. Coherent protocols; 8. The unit resource capacity region; Part IV. Tools of Quantum Shannon Theory: 9. Distance measures; 10. Classical information and entropy; 11. Quantum information and entropy; 12. The information of quantum channels; 13. Classical typicality; 14. Quantum typicality; 15. The packing lemma; 16. The covering lemma; Part V. Noiseless Quantum Shannon Theory: 17. Schumacher compression; 18. Entanglement concentration; Part VI. Noisy Quantum Shannon Theory: 19. Classical communication; 20. Entanglement-assisted classical communication; 21. Coherent communication with noisy resources; 22. Private classical communication; 23. Quantum communication; 24. Trading resources for communication; 25. Summary and outlook; Appendix A. Miscellaneous mathematics; Appendix B. Monotonicity of quantum relative entropy; References; Index.