Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

In this work, we study a recently proposed operational measure of nonlocality by Fonseca and Parisio [Phys. Rev. A 92 , 030101(R) (2015)] which describes the probability of violation of local realism under randomly sampled observables, and the strength of such violation as described by resistance to white noise admixture. While our knowledge concerning these quantities is well established from a theoretical point of view, the experimental counterpart is a considerably harder task and very little has been done in this field. It is caused by the lack of complete knowledge about the facets of the local polytope required for the analysis. In this paper, we propose a simple procedure towards experimentally determining both quantities for N-qubit pure states, based on the incomplete set of tight Bell inequalities. We show that the imprecision arising from this approach is of similar magnitude as the potential measurement errors. We also show that even with both a randomly chosen N-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost 100% of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.

Automated summary

This study investigates an operational measure of nonlocality proposed by Fonseca and Parisio, examining the probability and strength of violating local realism, and suggests a simple experimental procedure for determining these quantities for N-qubit pure states. The research shows that even with randomly selected pure states and measurement bases, experimental detection of violations of local realism is almost guaranteed.