1) Prerequisites
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 experience writing down correct and complete mathematical proofs. We will also offer some optional homework that will involve programming to explore mathematical concepts that we discuss in class. You can use any programming language of your choice.
Some prior exposure to quantum mechanics or information theory can be helpful, but is not necessary to follow the course.
2) Aim of the course
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 channels) and then discuss some more advanced topics (such as compression of quantum information and entanglement theory).
This course complements Ronald de Wolf's course on Quantum Computing (https://homepages.cwi.nl/~rdewolf/qc23fall.html). Students interested in writing a master's thesis in quantum information/computing are encouraged to follow both courses.
3) Rules about Homework/Exam
There will be a written exam at the end of the course. The final grade will be determined by the following formula:
60% exam grade + 40% max(homework grade, 5)
In addition, your exam grade alone has to be at least a 5.0. The same rule applies for the retake exam.
There will be bi-weekly homework problems, announced on the course homepage on Monday. You must submit your completed homework on ELO before the stated deadline. Assignments will be accepted late only if you have extenuating circumstances (such as sickness or family emergency) and provided you confirm with the lecturer before the deadline.
You are allowed to bring one self-prepared "cheat sheet" to the exam (A4 paper, hand-written, you can use both sides).
4) Lecture notes/Literature
Most relevant to this course:
* Last year's lecture notes and other course material
* Lectures notes of the UvA course Introduction to Information Theory (2020)
Supplementary literature:
* John Watrous, Theory of Quantum Information, lectures notes (https://cs.uwaterloo.ca/~watrous/TQI-notes/) and book (https://cs.uwaterloo.ca/~watrous/TQI/).
* Mark M. Wilde, Quantum Information Theory (https://arxiv.org/abs/1106.1445), Cambridge University Press (2013)
* Sumeet Khatri and Mark M. Wilde, Principles of Quantum Communication Theory (https://arxiv.org/abs/2011.04672), book draft (2020)
* John Preskill's lecture notes (http://theory.caltech.edu/~preskill/ph229/), Chapters 1–4 and 10
* Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)
* Fernando G.S.L. Brandao, Matthias Christandl, Aram W. Harrow, Michael Walter, The Mathematics of Entanglement (https://arxiv.org/abs/1604.01790)
* Roger A. Horn, Charles R. Johnson, Matrix Analysis, Cambridge University Press (2012)
* Michael Walter's lectures notes on Symmetry and Quantum Information (https://qi.ruhr-uni-bochum.de/qit18/) (2018)
- Docent: Jonas Helsen
- Docent: Maris Ozols