Entanglement and non-locality are different resources

Bell's theorem states that, to simulate the correlations created by measurement on pure entangled quantum states, shared randomness is not enough: some 'non-local' resources are required. It has been demonstrated recently that all projective measurements on the maximally entangled state of two qubits can be simulated with a single use of a 'non-local machine'. We prove that a strictly larger amount of this non-local resource is required for the simulation of pure non-maximally entangled states of two qubits |ψ(α)⟩ = cosα|00⟩ + sinα|11⟩ with .