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

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.