Bell-type inequality and quantum nonlocality in four-qubit systems

TL;DR

This paper introduces a Bell-type inequality for four-qubit systems, demonstrating its violation by various entangled states and exploring the relationship between entanglement and nonlocality.

Contribution

It presents a new Bell-type inequality for four-qubit states and analyzes its violation across different entangled states, revealing insights into quantum nonlocality.

Findings

Maximal violation by four-qubit maximal entangled state |G_m>

Violation observed in four-qubit W state and |G_{ab00}> states

Derived entanglement-nonlocality relationship for |G_{ab00}> states

Abstract

We present a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states $\left|G_{abcd}\right >$ [Phys. Rev. A 65, 052112 (2002)] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by so called "four-qubit maximal entangled state $\left|G_{m}\right >$" and it is also violated by the four-qubit W state and a special family of states $\left|G_{ab00}\right >$. Moreover, a useful entanglement-nonlocality relationship for the family of states $\left|G_{ab00}\right >$ is obtained.