Test of Genuine Multipartite Nonlocality Without Inequality

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In this letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all non-signaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the non-signaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any non-signaling local models, i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n ≥ 3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.