  The ground state entanglement entropy is studied in a many-body bipartite
quantum system with either a single or multiple conserved quantities. It is
shown that the entanglement entropy exhibits a universal power-law behaviour at
large $R$ -- the occupancy ratio between the two subsystems. Single and
multiple conserved quantities lead to different power-law exponents, suggesting
the entanglement entropy can serve to detect hidden conserved quantities.
Moreover, occupancy measurements allow to infer the bipartite entanglement
entropy. All the above results are generalized for the R\'enyi entropy.
