New Bell inequalities for three-qubit pure states

TL;DR

This paper introduces new Bell inequalities for three-qubit systems that can distinguish different entanglement classes and are violated by all generalized GHZ states, establishing a link between nonlocality and entanglement.

Contribution

The paper presents a novel set of Bell inequalities for three-qubit states that can differentiate between separable, biseparable, and genuinely entangled states, and extends these to n-qubit systems.

Findings

All generalized GHZ states violate these inequalities.

The inequalities can distinguish between different entanglement classes.

At least one inequality is violated by a genuinely entangled state.

Abstract

We introduce a set of Bell inequalities for a three-qubit system. Each inequality within this set is violated by all generalized GHZ states. More entangled a generalized GHZ state is, more will be the violation. This establishes a relation between nonlocality and entanglement for this class of states. Certain inequalities within this set are violated by pure biseparable states. We also provide numerical evidence that at least one of these Bell inequalities is violated by a pure genuinely entangled state. These Bell inequalities can distinguish between separable, biseparable and genuinely entangled pure three-qubit states. We also generalize this set to n-qubit systems and may be suitable to characterize the entanglement of n-qubit pure states.