The CHSH-Bell Inequality and Tsirelson's Bound with Postselection - Dominic Berry

We find the necessary and sufficient condition on postselection for the CHSH-Bell inequality to hold for local realistic theories. This condition is weaker than the usual fair sampling assumption, demonstrating that the CHSH-Bell inequality will be valid under a wider variety of types of loss than previously believed. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, if we restrict ourselves to a fixed set of measurements, it is possible for Tsirelson's bound to be violated while the CHSH-Bell inequality still holds for separable states. We present an experimentally feasible example for such violations.