Highly entangled, non-random subspaces of tensor products from quantum groups

In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of $d$-positive maps on matrix algebras is also presented.