Experimental tests of multiplicative Bell inequalities and the fundamental role of local correlations

Abstract

Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators within bipartite systems) has been recently proposed. For these new Bell parameters, it is relatively easy to find the classical and quantum, i.e., Tsirelson, limits. Here, we experimentally test the Tsirelson bounds of these inequalities using polarization-entangled photons for a different number of measurements (n), each party can perform. For n=2,3,4, we report the experimental violation of local hidden variable theories. In addition, we experimentally compare the results with the parameters obtained from a fully deterministic strategy, and observe the conjectured nature of the ratio. Finally, utilizing the principle of "relativistic independence"encapsulating the locality of uncertainty relations, we theoretically derive and experimentally test new and richer quantum bounds for both the multiplicative and the additive Bell parameters for n=2. Our findings strengthen the deep correspondence between local and nonlocal correlations, and pave the way for both theoretical (e.g., better understanding of nonlocal correlations) and practical (e.g., Bell tests and quantum technologies with inefficient detectors) applications.