Wringing out better Bell inequalities

Abstract

Local realism implies constraints on the statistics of two physically separated systems. These constraints, known collectively as Bell inequalities, can be violated by quantum mechanics. The standard Bell inequalities apply to a pair of two-state systems and constrain the value of some linear combination of correlation functions between the two systems. We generalize these standard Bell inequalities in two ways. First, we “chain” the Clauser-Horne-Shimony-Holt Bell inequality to obtain chained correlation Bell inequalities for two-state systems; we model a real experiment to show that these chained Bell inequalities lead to stronger quantum violations. Second, we formulate information-theoretic Bell inequalities, which are written in terms of the average information obtained in several measurements on a pair of physically separated systems (not just two-state systems); these information Bell inequalities have an appealing interpretation: if local realism holds, the two systems must carry an amount of information consistent with the inequality.