Experimental tests of Multiplicative Bell Inequalities

TL;DR

This paper experimentally tests new multiplicative Bell inequalities using entangled photons, confirming quantum violations and exploring bounds related to locality and nonlocal correlations, advancing understanding of quantum nonlocality.

Contribution

It provides the first experimental verification of Tsirelson bounds for multiplicative Bell inequalities and introduces new bounds based on relativistic independence principles.

Findings

Experimental violation of local hidden variable theories for n=2, 3, 4.

Comparison of quantum results with deterministic strategies.

Theoretical and experimental validation of new bounds for Bell parameters.

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 polarisation-entangled photons for 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 richer bounds for both the multiplicative and the additive Bell parameters for $n=2$. Our findings strengthen the correspondence between local and nonlocal correlations, and may pave the way for empirical tests of quantum mechanical bounds with inefficient detection systems.