Multipartite entanglement vs nonlocality for two families of $N$-qubit states

Abstract

Entangled states of multiple qubits can violate Bell-type inequalities indicating nonlocal behavior of multiqubit quantum correlations. We analyze the relation between multipartite entanglement and genuine multipartite nonlocality, characterized by Svetlichny inequality violations, for two families of $N-$qubit states. We show that for the generalized GHZ family of states, Svetlichny inequality is not violated when the $n-$tangle is less than $1/2$ for any even number of qubits. On the other hand, the maximal slice states always violate the Svetlichny inequality when $n-$tangle is nonzero, and the violation increases monotonically with tangle. Our work generalizes the relations between tangle and Svetlichny inequality violations previously derived for three qubits.