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Physical Review A

Genuine tripartite nonlocality for random measurements in Greenberger-Horne-Zeilinger-class states and its experimental test

Artur Barasiński, Antonín Černoch, Karel Lemr, Jan Soubusta

Published May 14, 2020• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.101.052109

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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.
Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.
From an operational criterion of physical reality, a quantifier of realism-based nonlocality was recently introduced for two-part quantum states. This measure has been shown to capture aspects that are rather different from Bell nonlocality. Here we take a step further and introduce a tripartite realism-based nonlocality quantifier. We show that this measure reduces to genuine tripartite entanglement for a certain class of pure tripartite states and manifests itself in correlated mixed states even in the absence of quantum correlations. A case study for noisy Greenberger-Horne-Zeilinger (GHZ) and WWW states points out the existence of scenarios where the realism-based nonlocality is monogamous.
In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.
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.
The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger (GHZ), W, and graph states under local decoherence processes. We derive lower bounds on the critical local-noise strength tolerated by the states before becoming local. In addition, for the whole noisy dynamics, we derive lower bounds on the corresponding nonlocal content for the three classes of states. All the bounds presented can be calculated efficiently and, in some cases, provide significantly tighter estimates than with any other known method. For example, they reveal that NNN-qubit GHZ states undergoing local dephasing are, for all NNN, nonlocal throughout all the dephasing dynamics.
Abstract In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in Salavrakos et al (2017 Phys. Rev. Lett. 119 040402) a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled Greenberger–Horne–Zeilinger-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.