| CS 798 – Advanced Research Topics | University of Waterloo |
This course presents a mathematical treatment of the theory of quantum information, with a focus on the development of concepts and methods that are fundamental to a broad range of studies in quantum algorithms and complexity, quantum cryptography, and quantum Shannon theory.
The course is intended for graduate students at the Masters or PhD level, and it is recommended that students have previously taken an introductory course in quantum computing at the undergraduate or graduate level.
| 1. | Mathematical preliminaries – part 1. | [ps, pdf] |
| 2. | Mathematical preliminaries – part 2. | [ps, pdf] |
| 3. | Registers, reduced states, and measurements. | [ps, pdf] |
| 4. | Pure states, purifications, and fidelity. | [ps, pdf] |
| 5. | Naimark's Theorem; Characterization of quantum operations. | [ps, pdf] |
| 6. | Examples of states, measurements, and operations. | [ps, pdf] |
| 7. | Entropy and compression. | [ps, pdf] |
| 8. | Properties of the von Neumann entropy. | [ps, pdf] |
| 9. | Strong subadditivity of the von Neumann entropy. | [ps, pdf] |
| 10. | Holevo's Theorem and Nayak's Bound. | [ps, pdf] |
| 11. | Majorization for real vectors and Hermitian operators. | [ps, pdf] |
| 12. | Separable operators. | [ps, pdf] |
| 13. | Separable super-operators and the LOCC paradigm. | [ps, pdf] |
| 14. | Pure state entanglement transformation. | [ps, pdf] |
| 15. | Measures of entanglement. | [ps, pdf] |
| 16. | The partial transpose and bound-entangled states. | [ps, pdf] |
| 17. | LOCC and separable measurements. | [ps, pdf] |
| 18. | Super-operator norms and distinguishability. | [ps, pdf] |
| 19. | Alternate characterization of the diamond norm. | [ps, pdf] |
| 20. | Semidefinite programming. | [ps, pdf] |
| 21. | The quantum de Finetti theorem. | [ps, pdf] |
All 21 lectures in one file [ps, pdf].
| Problem set 1 [ps, pdf]. |
| Problem set 2 [ps, pdf]. |
| Problem set 3 [ps, pdf]. |