Clauser-Horne-Shimony-Holt-type Bell inequalities involving a party with two or three local binary settings

Abstract

We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer.

Connector tensor networks: a renormalization-type approach to quantum certification

“…It is worth remarking that the notion of composing m → 1 connectors to form new Bell inequalities is implicit in the work of Wu et al [37]. There, the authors propose a scheme to generate a new (m + 1)-partite new Bell inequality in the two-input/two-output Bell scenario, given two m-partite Bell inequalities.…”

“…The tensors defining box (36) are given by: Λ [1] a,x = 1 2 x| a|, Finally, it can be verified that an MPS representation for box (37) is given by the matrices: Λ [1] a,x = x| a|,…”

Experimental violation of the local realism for four-qubit Dicke state

“…For arbitrary many observers, each choosing between two local dichotomic observables, the complete set of tight CHSH-type Bell inequalities has been obtained [7][8][9]. Such inequalities have been pointed out to possess a common structure [10]. However, the explicit expressions of Bell inequalities are too complicate to be used to verify the violation of local realism.…”

Compact Bell inequalities for multipartite experiments

“…In the simpler case of three qubits, with to numerical methods one may obtain all facets of correlation polytope [14,15]. The geometrical concept of correlation polytopes is also helpful for building some new Bell inequalities for more complicated cases [8,[16][17][18].Nevertheless, observations of violations of local realism in the case of multipartite correlations are a challenging task. Generation of multipartite entangled states is a challenge itself [19].…”

“…Such inequalities have been pointed out to possess a common structure [8]. However, in the case of more complicated situations (i.e., with more local settings, more parties, or more measurement outcomes), it is still an open task to obtain the complete set of tight Bell inequalities.…”