Entangling quantum information theory and Fourier multipliers on operator algebras

One of the most fundamental questions in quantum information concerns with the amount of information that can be transmitted reliably through a quantum channel. For that, many capacities and entropies were introduced for describing the capability of the quantum channel for delivering information from the sender to the receiver. In this talk, we will explain how to obtain the exact values of some of these quantities for large classes of channels by using the theory of Fourier multipliers on quantum groups or more abstract structures.