MATH 595: Quantum channels I
Representations and properties

Spring term 2021 (weeks 1-8): Tue & Thu, 12:30-01:50. All lectures held online.
Instructor: Felix Leditzky (homepage)
Zoom link:
Password will be distributed to registered students by email. If you're interested in attending the course, please send me an email at <mylastname> to request the password.
Office hours: via Zoom, by appointment only.


Course description: This course gives an introduction to the theory of quantum channels in the finite-dimensional setting of quantum information theory. We discuss the various mathematically equivalent representations of quantum channels, focus on some important subclasses of channels, and make connections to the theory of majorization and covariant channels.

Prerequisites: MATH 415 or MATH 416
Throughout the course I will draw connections to quantum information theory, in particular the subfield of "quantum Shannon theory" that is concerned with the study of capacities of quantum channels amongst other things. However, no prior knowledge in this area is necessary to follow the course.

Grading policy: There will be no homework assignments or written exams for this course. Grading will be based on active class participation. However, I will provide exercise sheets, and it is strongly recommended to attempt to solve them.

Remark: This is a half-course, spanning the first 8 weeks of the term. I will teach a follow-up course Quantum channels II - data-processing, recovery channels, and quantum Markov chains in weeks 9-16. While attendance of both courses is recommended, the second course will be fairly independent from this course.

Table of contents


Jacob Beckey has generously committed to typing up the lecture notes in LaTeX, which are available on GitHub.

Throughout the lecture I am trying to give some quantum information-theoretic context while discussing quantum channels and their properties. Unfortunately, it is beyond the scope of this lecture to discuss these information-theoretic aspects in more detail. Along with Mark M. Wilde's book on Quantum Information Theory (see the course literature below), the lecture Theory of Quantum Communication (Fall 2020) taught by Debbie Leung at the University of Waterloo is an excellent resource to learn more about this topic.



Email: <mylastname>

Postal address:
Illini Hall, Office 341B
725 S. Wright Street
Champaign, IL 61820