Optimal tests of genuine multipartite nonlocality

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.

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

“…[10][11][12] As the strongest notation of multipartite non-locality, genuine multipartite non-locality (GMNL) is one of the most fundamental non-classical features of multipartite systems and has attracted considerable attention. [13][14][15][16][17] Initially, Svetlichny [3] provided a Bell-type inequality to detect genuine tripartite non-locality and later the Svetlichny inequality has been generalized to arbitrary parties [18,19] and arbitrary dimensions. [20] Nevertheless, the task of detection and characterization of GMNL is demanding, as the complexity of the possible states of the systems and sets of correlations grows exponentially with the number of parties involved in multipartite Bell scenario.…”

“…Multipartite Bell-type inequalities are an effective approach to describe multipartite correlations and provide insight into the rich structure of multipartite scenarios and thus much effort has been devoted to this research with a desire to gain a better understanding of GMNL. [17,[21][22][23] Furthermore, the significant advantage of GMNL lies in certifying the presence of genuine multipartite entanglement in a device-independent way by observing the violation of some genuine multipartite Bell-type inequalities. For progress in the experimental aspects of multipartite entanglement, see refs.…”