A Hadamard matrix is a square matrix of complex numbers whose entries have modulus 1, and whose columns are pairwise orthogonal. Hadamard matrices appear all over mathematics, and are well known in the field of operator algebras as basic building blocks in subfactor theory. In this talk I will introduce various notions of notions of quantum symmetries and quantum equivalences of Hadamard matrices using ideas from quantum group theory. These symmetries, in the case of finite order (i.e., Butson-type) Hadamard matrices, turn out to have interesting applications in quantum information theory.

This is joint work with Daniel Gromada, Roberto Hernandez-Palomares, and Nicky Priebe.