Entanglement and non-locality are different resources

Abstract

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 $\ket{ψ(α)}= \cosα\ket{00}+\sinα\ket{11}$ with $0<α\lesssim\fracπ{7.8}$.

8 pages, 3 figures