Nonlocality of three-qubit Greenberger-Horne-Zeilinger-symmetric states

TL;DR

This paper analyzes the nonlocality properties of GHZ-symmetric three-qubit mixed states, deriving conditions for their violation of Bell inequalities and exploring the relationship between entanglement and nonlocality.

Contribution

It provides analytical expressions for Bell inequality violations and clarifies the link between entanglement and nonlocality in GHZ-symmetric states.

Findings

Genuine entanglement is necessary for standard nonlocality.

Conditions for nonlocality violations are derived analytically.

Entanglement is not sufficient alone to guarantee nonlocality.

Abstract

Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent article [Phys. Rev. Lett. \textbf{108}, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three qubit states with the same symmetry as Greenberger-Horne-Zeilinger state known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expressions of maximum violation value of most efficient Bell inequalities we obtain the conditions of standard nonlocality and genuine nonlocality of this class of states. Also relation between entanglement and nonlocality is discussed for this class of states. Interestingly, genuine entanglement of GHZ-symmetric states is necessary to reveal standard nonlocality. However, it is not sufficient to exploit the same.