Role of Particle Entanglement in the Violation of Bell Inequalities

Abstract: Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule imposes a constraint on feasible local operations. As we show in an example, the necessary particle entanglement might solely result from their indistinguishability. Our result reveals a fundamental relation between the non-locality and the particle entanglement.