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

Abstract

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.

Optimal tests of genuine multipartite nonlocality

“…As we see in Tab. I, despite the great limitations of the problem [25,31], the estimated probability of violation (hereafter denoted as P I V ) is surprisingly consistent with the previous calculations for almost all Bell experiments. In particular, a very good consistency is observed for the L and N S 2 scenarios.…”

“…Our calculations provide that in all scenarios discussed above one can clearly distinguish a so-called dominant Bell inequality, i.e. the family of equivalent Bell inequalities, which are most often violated for a given Bell experiment [25,31]. For the the GHZ and |ψ s states such dominant position is reserved for the 4th facet inequality (I L 4 ) for the L scenarios, the 4th facet inequality (I N S2…”

“…Recently, the violations of local realism by families of multipartite quantum states has been analysed numerically [23] and experimentally [24][25][26], showing that the probability of violation can also serve as a witness of GME. A notable advantage of these approaches is that the probability of violation operates in a so-called reference-frame-independent mode [27][28][29], lowering requirements for alignment and calibration of remote devices [26].…”

Measuring concurrence in qubit Werner states without aligned reference frame

“…The function ω(ρ, Ω) is an indicator function that takes the value 1 whenever the generated behavior is nonlocal and 0 otherwise. What is important, in this approach the nonlocal correlations are quantified without any prior assumptions about specific Bell inequalities [34,61,62]. In other words, the generated behavior is nonlocal if at least one inequality of the suitable set of Bell inequalities is violated.…”

“…The latter one requires the accumulation of data on the strength of violation of local realism for sequence of randomly chosen measurements. In a typical experimental investigation of p V [31,34,62] such a set is known without any additional effort.…”