Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states

TL;DR

This paper explores the connection between tripartite entanglement and nonlocality in 3-qubit GHZ-class states, deriving analytical relations and identifying conditions for Svetlichny inequality violation.

Contribution

It provides an analytical link between 3-tangle and Svetlichny inequality violation for generalized GHZ states and characterizes nonlocality in maximal slice states.

Findings

States with 3-tangle < 1/2 do not violate Svetlichny inequality

Maximal slice states violate Svetlichny inequality proportionally to entanglement

Analytical relation between 3-tangle and nonlocality in GHZ-class states

Abstract

We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for 3-qubit pure states in the GHZ class. We consider a family of states known as the generalized GHZ states and derive an analytical expression relating the 3-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with 3-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states do violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized GHZ and maximal slice states.