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

Dilip Paneru,Amit Te'Eni,Ebrahim Karimi,Bar Y Peled,Eliahu Cohen,Avishy Carmi,Yingwen Zhang,James Hubble

doi:10.1103/physrevresearch.3.l012025

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.

Highlights

Ever since quantum mechanics was introduced to describe the subatomic world, the foundational aspects, most notably the nondeterministic nature of experimental outcomes, have always been a topic of discussion among physicists and philosophers [1]
This discrepancy is most conveniently illustrated by Bell parameters, i.e., measurable quantities whose values must be bounded to a certain extent in any local hidden variable theory, but can exceed these bounds according to quantum mechanics [5]
The experimental results show that the multiplicative Bell parameters go beyond their classical limits, again falsifying local realism

Summary

INTRODUCTION

Ever since quantum mechanics was introduced to describe the subatomic world, the foundational aspects, most notably the nondeterministic nature of experimental outcomes, have always been a topic of discussion among physicists and philosophers [1]. In 1964 John Bell showed that there exist experiments for which any local hidden variable theory must disagree with quantum mechanics about the predicted outcome [4]. For the simplest case where Alice and Bob measure two random variables each, it was proven that the bound for classical correlations is strictly less than that for quantum correlations These multiplicative Bell inequalities were shown to be more robust to detector inefficiency than the additive ones [20], which is another useful property of the proposed nonlinear inequalities. Based on relativistic independence we propose and put to test new Tsirelson bounds that are richer than those derived in the past This shows the interplay between local and nonlocal correlations, which has both fundamental and applicative implications

THEORY

EXPERIMENT

LOCALITY OF UNCERTAINTY AND RICHER QUANTUM BOUNDS

CONCLUSION