It is believed that the ground state entanglement entropy for a local gapped Hamiltonian satisfies an area law. That is, if we divide such a system in two parts A and B, then S(ρA)=−Tr[ρAlog(ρA)] is proportional to the area of the boundary separating A and B, where ρA=TrB(ρAB) and ρAB is the ground state density matrix. Does it mean that we can perform unitary operations localized near the boundary and make the ground state a product state of the form ρ′AB=ρ′A×ρ′B ?