Symmetry Resolved Multipartite Entanglement Entropy

We perform the symmetry resolution of a multipartite entanglement measure, namely the global entanglement $Q$ introduced by Meyer and Wallach [2002, J. of Math. Phys., 43, pp. 4273] for all systems of distinguishable particles hosting a locally acting symmetry. For an ensemble of Haar random states we find agreement with equipartition, with leading order behaviour and finite size corrections which follow a power law scaling with the number of local degrees of freedom. Implications of this result for the general symmetry-resolved multipartite entanglement paradigm are discussed and some possible experimental verification methods are presented.