Greenberger-Horne-Zeilinger States: Their Identifications and Robust Violations

Abstract

The $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states are the maximally entangled states of $N$ qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, we show that the $N$-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any $N$-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality, in which the maximal violation of Bell's inequality can be robust under some specific noises adding to the $N$-qubit GHZ states.

arXiv comment5 pages

References in corpus (10)

• Quantum entanglement
• Bell nonlocality
• Symmetries of the Bell correlation inequalities
• Spectral decomposition of Bell's operators for qubits
• Optimal verification of entangled states with local measurements
• Verification of Many-Qubit States
• Efficient Verification of Hypergraph States
• Efficient verification of Dicke states
• Experimental Optimal Verification of Entangled States using Local Measurements
• Characterization of maximally entangled two-qubit states via the Bell-Clauser-Horne-Shimony-Holt inequality