These lecture notes may be used and distributed freely, for individual study or by course instructors. They may not be sold.

These are rather old lecture notes for the course CS 766/QIC 820 Theory of Quantum Information, taught at the University of Waterloo in odd-numbered fall terms (2011, 2013, … , 2021). They are not currently being maintained (although I do hope to update them in the future), and I believe that everything of value that they cover is done better in my book The Theory of Quantum Information. I encourage you to use that resource instead, but have made these notes available for those that prefer them or wish to examine how different topics are covered lecture by lecture.

Latest update: December 1, 2011

All 22 lectures in one file (197 pages) [pdf]

1. Mathematical preliminaries (part 1) [pdf]
2. Mathematical preliminaries (part 2) [pdf]
3. States, measurements, and channels [pdf]
4. Purifications and fidelity [pdf]
5. Naimark’s theorem; characterizations of channels [pdf]
6. Further remarks on measurements and channels [pdf]
7. Semidefinite programming [pdf]
8. Semidefinite programs for fidelity and optimal measurements [pdf]
9. Entropy and compression [pdf]
10. Continuity of von Neumann entropy; quantum relative entropy [pdf]
11. Strong subadditivity of von Neumann entropy [pdf]
12. Holevo’s theorem and Nayak’s bound [pdf]
13. Majorization for real vectors and Hermitian operators [pdf]
14. Separable operators [pdf]
15. Separable mappings and the LOCC paradigm [pdf]
16. Nielsen’s theorem on pure state entanglement transformation [pdf]
17. Measures of entanglement [pdf]
18. The partial transpose and its relationship to entanglement and distillation [pdf]
19. LOCC and separable measurements [pdf]
20. Channel distinguishability and the completely bounded trace norm [pdf]
21. Alternate characterizations of the completely bounded trace norm [pdf]
22. The finite quantum de Finetti theorem [pdf]

©2020 John Watrous