Quantum non-locality and entanglement 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 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 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 $\ket{\psi(\alpha)}= \cos\alpha\ket{00}+\sin\alpha\ket{11}$ with $0<\alpha\lesssim\frac{\pi}{7.8}$.