Families of expander graphs were first constructed by Margulis from discrete groups with property (T). Within the framework of quantum information theory, several authors have generalised the notion of an expander graph to the setting of quantum channels. In this work, we use discrete quantum groups with property (T) to construct quantum expanders in two ways. The first approach obtains a quantum expander family by constructing the requisite quantum channels directly from finite-dimensional irreducible unitary representations, extending earlier work of Harrow using groups. The second approach directly generalises Margulis’ original construction and is based on a quantum analogue of a Schreier graph using the theory of coideals. To obtain examples of quantum expanders, we apply our machinery to discrete quantum groups with property (T) coming from compact bicrossed products. ... Read more

This mini-workshop brought together a rich and varied crosssection of young and active researchers working on operator algebraic aspects of quantum group theory. The primary goals of this meeting were to highlight the state-of-the-art results on the subject and to trigger new research by advertising some of the main open directions in operator algebraic quantum group theory: classification problems for C_- and von Neumann algebras, relations to free/non-commutative probability, applications in quantum information theory, and the creation of new quantum groups and potential classification results for subclasses of quantum groups ... Read more