International workshop on "Quantum Physics and Geometry"

PhD Course:
Quantum information theory and geometry

JM Landsberg (Texas A&M, USA)

Quantum information theory is  at the intersection of physics, computer science and mathematics. While it is little understood, what we know already may have a dramatic impact on our lives. Efforts are now being made to build a quantum computer, which, if successful, would in particular end the security of public key cryptography among many other things. At the present, we have very little knowledge of what a quantum computer can and cannot compute efficiently. Much research remains to be done.

This course will discuss the physics of information, and the mathematics needed to study it. The first half will cover background material from physics and computer science. It will give an overview and foundation of the subject. The second half will be an in-depth study of geometry and representation theory useful for quantum information theory. The mathematics covered will  prepare students to do research in this exciting and important area.

The primary target of the lectures are first year PhD students. However given its timely and interdisciplinary nature, it should also attract  students and  faculty in mathematics, physics and computer science.

Topics (approximately 5 hours of lecture each):
  1. Classical information theory (Shannon capacity, complexity).
  2. Quantum information theory and its connections to probability.
  3. Quantum complexity and algorithms.
  4. Representation theory for quantum information
  5. Algebraic geometry for quantum information.
Web Page on the UniTn Doctoral School in Mathematics.

Schedule of the course:

Material for the course will be drawn from several sources, including:

First week: