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

Abstract

We present a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states $|G_{abcd}⟩$ [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 $|G_m⟩$" and it is also violated by the four-qubit W state and a special family of states $|G_{ab00}⟩$. Moreover, a useful entanglement-nonlocality relationship for the family of states $|G_{ab00}⟩$ is obtained.

6 pages, 2 figures

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• Entanglement measure and quantum violation of Bell-type inequality for a family of four-qubit entangled states
• Violation of generalized Bell inequality and its optimal measurement settings
• Strong quantum nonlocality without entanglement in every $(n-1)$-partition
• Strongest quantum nonlocality in $N$-partite systems