MATH 595: Quantum channels II
Data-processing, recovery channels, and quantum Markov chains

Spring term 2021 (weeks 9-16): 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 Markov chains in the finite-dimensional setting of quantum information theory. We first discuss the quantum relative entropy and its fundamental property, the data-processing inequality, and give a proof of this inequality that naturally leads to equality conditions and the concept of recovery channels. Specializing this analysis to the partial trace, we obtain the strong subadditivity property of the von Neumann entropy, as well as a natural definition of quantum Markov chains. We then review a structure theorem for quantum Markov chains, the fundamental differences to classical Markov chains, and - time permitting - venture into the active research topic of approximate quantum Markov chains.

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 weeks 9-16 of the term. The first part of this course is Quantum channels I - Representations and properties in weeks 1-8. While attendance of both courses is recommended, this course will be fairly independent from the first one.

Table of contents




Email: <mylastname>

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