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.
Highlights
Nonlocality is arguably one of the most striking aspects of quantum mechanics, dramatically defying ourYet another possibility to quantify the nonlocal correlations of complex states is based on the probability that random measurements generate nonlocal statistics
As the (N − 2) single measurements Ej(i) cannot cause any violation of local realism, it implies that the nonlocal correlations witnessed by Io(Npt) have a two-qubit CHSH origin
In this paper we investigated the nonlocal fraction and the nonlocality strength as two important quantities characterizing nonlocal correlations of the quantum states
Summary
Nonlocality is arguably one of the most striking aspects of quantum mechanics, dramatically defying our. Note a recent theoretical work in the multipartite scenario which investigates Bellnonlocal correlations using linear programming and specific Bell inequalities as well by having the parties performing their measurements in a randomly chosen triad instead of randomly chosen bases [22] This geometric approach has no direct experimental implementation what causes a lack of experimental studies of the subject. It is because frequencies obtained in measurements are subject to Poissonian statistics, which can lead to the violation of local realism with the state visibility equal to 0, due to the inability to construct a correct joint probability distribution (see [23] for a more detailed discussion) These problems can be avoided by processing the collected experimental data using maximum-likelihood [24] or device-independent point estimation [25] methods. Our predictions were investigated experimentally for the three-qubit case, showing a good agreement with theoretical results
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