## Short course: **A Noisy Tour of Quantum Information**

Mary Beth Ruskai (Research Professor, Tufts University, Medford (MA), and Mittag-Leffler Institute)

November 15-16. 2010, University of Helsinki

### Time and place

Monday November 15, 10-12 in lecture room C124 (Exactum)

Tuesday November 16, 10-12 in lecture room D123 (Exactum)

### Abstract

Quantum information theory describes the use of quantum effects for computation, communication, and encryption. Although building a quantum computer remains a formidable challenge, practical cryptographic devices already exist. The study of problems in quantum information theory draw upon techniques from many different areas of mathematics including, operator algebras, operator spaces, non-commutative probability and operator inequalities, high-dimensional convex geometry, classical probability and random matrices, combinatorics and coding theory, group representations, and much more.

Any device which transmits quantum information needs to deal with the effects of noise. These lectures will give an overview of noise models, quantum Shannon theory and quantum error correction. Although none of these topics can be treated in depth, an introduction to basic concepts will be provided in a way that demonstrates how different areas of mathematics come into play. In each case below, I will try to indicate how some high-powered mathematical tools enter and provide references.

Tentative plan of the lectures:

Lecture 1. Introduction and noise models.

Lecture 2. Quantum Shannon theory.

Lecture 3. Basics of quantum error correction.

Lecture 4. Recent work using quantum codes to solve an old problem from quantum chemistry.