The bipartite von Neumann entanglement entropy S is defined as the von Neumann entropy of either of its reduced states, since they are of the same value (can be proved from Schmidt decomposition of the state with respect to the bipartition); the result is independent of which one we pick. That is, for a pure state ρ ρ A B = | Ψ Ψ ⟩ ⟩ ⟨ ⟨ Ψ Ψ | A B , it is given by: