Quantum automorphism groups of trees

We give a characterization of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a quantum version of Jordan's theorem for the automorphism groups of trees. We use ideas from algebraic combinatorics, quantum groups, and quantum information theory. This is one of the first characterizations of quantum automorphism groups of a natural class of graphs with quantum symmetry.