Optimal Bell Tests Do Not Require Maximally Entangled States

Any Bell test consists of a sequence of measurements on a quantum state in spacelike separated regions. Thus, a state is better than others for a Bell test when, for the optimal measurements and the same number of trials, the probability of existence of a local model for the observed outcomes is smaller. The maximization over states and measurements defines the optimal nonlocality proof. Numerical results show that the required optimal state does not have to be maximally entangled.

Figure 1

KL divergence for Bell tests using two projective measurements under the mentioned assumptions. Circles correspond to the optimal state $|{\Psi }_d⟩$, while crosses to the maximally entangled state $|{\Phi }_d⟩$. In the inset, the entropy of entanglement for $|{\Psi }_d⟩$ is shown.