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arXiv:2009.11691 · Quantum

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

Artur Barasiński, Antonín Černoch, Wiesław Laskowski, Karel Lemr, Tamás Vértesi, Jan Soubusta

Published Apr 14, 2021• 8 citations
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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.

DOI
10.22331/q-2021-04-14-430

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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.
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 NNN-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 NNN-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost 100%100\%100% of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.
In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to seven qubits. As a result, in the first part of this manuscript, we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behavior with both random state and measurement. Although this typicality is slightly above 5.3% for two qubits, for a modest increase in the number of involved particles it quickly surpasses 99.99%.
We present a comprehensive numerical analysis of violations of local realism by tripartite generalized Greenberger-Horne-Zeilinger states. As an indicator of nonlocality we use the nonlocal fraction which describes the probability of violation of local realism under randomly sampled observables. We compare two kinds of local realism based on standard and hybrid local--nonlocal models. As a result, we show a great disproportion of the results determined for both models. Although the nonlocal fraction for standard local realism and tripartite generalized Greenberger-Horne-Zeilinger states significantly increases compared to the bipartite Clauser-Horne-Shimony-Holt scenario, the genuine tripartite nonlocality (the strongest form of nonlocal correlations) is observed with probability much smaller than its bipartite counterpart. Furthermore, when the effects of decoherence on these states are introduced, such disproportion becomes significantly greater. Finally, we present the statistical relevance of various classes of tight Bell inequalities as they are of paramount importance for practical experimental investigation of all problems discussed in this paper. We also propose the nonlocal fraction of hybrid local--nonlocal realism as a measure of genuine tripartite entanglement.
We show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially separated parties who perform local measurements on a maximally entangled state using randomly chosen measurement bases can, with significant probability, generate nonclassical correlations that violate a Bell inequality. For n parties using a Greenberger-Horne-Zeilinger state, this probability of violation rapidly tends to unity as the number of parties increases. We also show that, even with both a randomly chosen two-qubit pure state and randomly chosen measurement bases, a violation can be found about 10% of the time. Among other applications, our work provides a feasible alternative for the demonstration of Bell inequality violation without a shared reference frame.
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove that this measure satisfies some natural properties for an operational measure of nonlocality. Then, we show that for pure states of two qubits the measure is monotonic with entanglement for all correlation two-outcome Bell inequalities: for all these inequalities, the more the state is entangled, the larger the probability to violate them when random measurements are performed. Finally, we extend our results to the multipartite setting.
Abstract The utilization of higher-dimensional systems holds promise for unveiling novel phenomena and enhancing the efficacy of practical tasks, such as entanglement-based quantum cryptography. However, detecting quantum correlations within qudit systems poses a formidable challenge. In this study, we delve into the intricacies of Bell’s nonlocality within higher-dimensional systems. We introduce a novel correlation function and leverage it to construct a family of Bell inequalities adapted for quantum systems of arbitrary dimensionality. By gauging the probability of local realism violation under random measurements as our primary metric, we explore the relation between pure state entanglement and nonlocality. Our findings align closely with predictions derived from the comprehensive polytope analysis via linear programming methods. While our focus predominantly centers on the two-qudit scenario, our methodology readily extends to the N-partite case, accommodating an arbitrary number of measurements per party.