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

Abstract

Quantum states of multiple qubits can violate Bell-type inequalities when there is entanglement present between the qubits, indicating nonlocal behaviour of 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 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 when the number of qubits is even. Our work generalizes the relations between tangle and Svetlichny inequality violation previously derived for three qubits.