With the birth of Quantum Mechanics a century ago, our understanding of the physical world has profoundly expanded, and so has our understanding of information. While a classical bit assumes only discrete values, represented by the binary values zero and one, a quantum-mechanical bit or "qubit" can assume a continuum of intermediate states. Quantum Information Theory studies the remarkable properties of this new type of information, ways of processing it, as well as its advantages and limitations.
This course offers a mathematical introduction to Quantum Information Theory. We will start with the fundamentals (such as quantum states, measurements, and entropy) and then discuss some more advanced topics (entanglement theory and quantum communication) and techniques (representation theory or semidefinite programming).
This course complements Ronald de Wolf's course on Quantum Computing. Neither course requires the other, but students interested in writing a thesis in quantum information/computing are encouraged to follow both courses.
Familiarity with linear algebra (in finite dimensions) and probability theory (with finitely many outcomes), but we will recap the more difficult bits in class. Concretely this means the material in Chapter 2.1 and Appendix 1 of "Quantum Computation and Quantum Information" by Nielsen and Chuang. (For a more formal account, see Sections 1.1 and 1.2.2 of "Theory of Quantum Information" by Watrous.) Please have a brief look at last year's lecture notes to get more of an impression. In addition, you should have some experience writing down correct and complete mathematical proofs. Some of the homework will also involve programming to explore mathematical concepts that we discuss in class. You can use a programming language of your choice; we will give solutions in Python.
Some prior exposure to quantum mechanics or information theory can be helpful, but is not necessary to follow the course.
Michael Walter and Maris Ozols
Teaching assistants: Freek Witteveen, Dmitry Grinko