A group theoretic calculation of multi-invariants of some stabilizer states

We study multi-invariants—a multi-partite generalization of Renyi entropies—of simple stabilizer states, for an arbitrary replica symmetry group. We develop a group theoretic technique for evaluating such invariants, which operates on the replica group and involves counting intersections among its cosets. Our techniques streamline the calculations of multi-invariants for graph states with two GHZ-like nodes and for certain generalizations thereof. The methodology developed here is most suitable when the quantum state is simple but flexibility over the replica group is desired.