# Quantum Information Theory

**Lecturers:** Maris Ozols and Michael Walter

**Teaching assistants:** Arjan Cornelissen and Freek Witteveen

**Schedule:** Mon 14:00-16:45 (SP A1.04), Spring 2019

**Further information:** MasterMath, DataNose, Studiegids

The MasterMath course page is the primary source for all course material.

## Course description

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 (semidefinite programming and representation theory).

This course will complement Ronald de Wolf’s course on Quantum Computing. Students interested in writing a thesis in quantum information theory are encouraged to follow both courses.

## Prerequisites

Familiarity with basic linear algebra and probability theory. Concretely, you should be familiar with the majority of the material in Sections 1.1.2 and 1.2.2 of John Watrous’ textbook (see below). We will briefly remind you of the more difficult bits in class. Prior exposure to the formalism of quantum mechanics or information theory will be very helpful, but not necessary.

## Homework and Exam

The final grade will be determined 40% by the homework grade and 60% by the final exam. There will be one problem set per week.

## Lecture Notes and Literature

The course will be roughly based on John Watrous’ textbook “The Theory of Quantum Information”, available online.

In addition, we will offer handwritten lecture notes after each class.

Additional references that may be useful:

- Mark M. Wilde, Quantum Information Theory, Cambridge University Press (2013)
- 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
- Roger A. Horn, Charles R. Johnson, Matrix Analysis, Cambridge University Press (2012)
- Lectures notes of the UvA course Symmetry and Quantum Information (2018)

## FAQ

*Is this the first time this class is offered?*

This is the first time this class is offered at the University of Amsterdam. Last year, Michael Walter offered a related course on Symmetry and Quantum Information.

*Can this course only be taken by students enrolled in the Master’s of Mathematics?*

No! You should be able to take the course as part of the “free choice” component of your Master’s program (in which case you can get credit) or as an additional course (which should show up on your Master’s diploma as well).

Moreover, auditors are very welcome, too, so feel free to drop by to watch a particular lecture if there’s a topic that interests you particularly.

*Where can I learn more advanced material?*

Attend the QuSoft seminar and write a Master’s thesis at QuSoft!