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 nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling 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.
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 nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling 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.
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.
In a multipartite setting, it is possible to distinguish quantum states that are genuinely n-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely n-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of n-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations.
Nonlocal correlations as revealed by the violations to Bell inequalities are incompatible with local models without any nonlocal correlations. However some tripartite entangled states, e.g., symmetric pure states, exhibit a stronger nonlocality even incompatible with hybrid local/nonlocal models allowing nonlocal correlations between any two parties. Here we propose a three-particle Hardy-type test without inequality, as illustrated by a gedanken experiment, that is failed by all non-signaling local models while is passed by all tripartite entangled asymmetric pure states. Our result implies that every tripartite entangled state, regardless of the dimensions of the underlying Hilbert spaces, passes a Hardy-type test and therefore is genuine tripartite nonlocal. Maximal success probability and a generalization to multipartite cases of our test are also presented.
Abstract We propose an optimal and efficient numerical test for witnessing genuine multipartite nonlocality based on a geometric approach. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal models. While our knowledge concerning these models is well established for Bell-type scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine n-way nonlocal correlations for various states of three qubits and qutrits. Apart from the fundamental problem of characterizing genuine multipartite nonlocal correlations, the extension of the number of measurements beyond two is also of practical importance. As a measure of nonlocality, we use the probability of violation of local realism under randomly sampled observables, and the strength of nonlocality, described by the resistance to white noise admixture. In particular, we analyze to what extent the Bell-type scenario involving two measurement settings can be used to certify genuine n-way nonlocal correlations generated for more general models. In addition, we propose a simple procedure to detect such nonlocal correlations for randomly chosen settings with an efficiency of up to 100%. Due to its near-perfect efficiency, our method may open new possibilities in device-independent quantum cryptography applications where strong nonlocality between all partners is required.
We propose a hierarchy of Bell-type inequalities for arbitrary n-partite systems that identifies the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling m locality, we show that the observed joint probabilities in any nonsignaling m-local realistic models should satisfy the $(m\ensuremath{-}1)\mathrm{th}$ Bell-type inequality. When m=2, the corresponding inequality reduces to the one shown earlier [Q. Chen et al., Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when m=n, the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been investigated separately. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources enables the certification of the nonclassicality of all sources. In this Letter, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations that cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high-fidelity photonic quantum network by violating a single network Bell inequality.