Jason Crann: Quantum Channels Arising From Abstract Harmonic Analysis

Jason Crann, Carleton University

Abstract

The recent representation theory surrounding locally compact groups has initiated several new connections between harmonic analysis and quantum information. In this talk, we will demonstrate how one can use this theory to generate two intriguing classes of quantum channels for every finite group. We will then explore several concrete examples and discuss their applications to quantum error correction and to the convex structure of bistochastic channels, providing a new class of counter examples to the recently solved Asymptotic Quantum Birkoff Conjecture.

This is joint work with Matthias Neufang.