Speaker: **Benoit Collins** (Kyoto University)

Title: Quantum channels from the free orthogonal quantum group

Time/Date: 4:45-6:15pm, Wednesday, January 6, 2016

Room: 118 Math. Sci. Building

Abstract:
given two finite dimensional Hilbert spaces V_{1} and V_{2},
a crucial problem in quantum information theory is to find vector subspaces
H of V_{1}⊗ V_{2} of large relative dimension that are
highly entangled. The most powerful methods available so far for this
purpose use random techniques. However, like in classical information
theory, there is a need and an interest for non-random examples. In this
talk, we will explain why the representation theory of the free orthogonal
quantum group yields new interesting examples --- thanks, in particular,
to the rapid decay property for quantum groups. In turn, we will study
the properties of associated quantum channels. This is a joint work in
progress with Michael Brannan (Texas A & M).