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

TL;DR

This paper introduces a simple generalized CHSH inequality to identify N-qubit GHZ states through maximal violations, and demonstrates their robust violation under certain noise conditions, aiding experimental verification.

Contribution

It proposes a new, simple generalized CHSH inequality for identifying GHZ states and shows their robust violation under specific noise conditions.

Findings

GHZ states can be identified via maximal violations of the generalized CHSH inequality.

The generalized CHSH inequality involves only four correlation functions, simplifying experiments.

Maximal violation of Bell's inequality remains robust under certain noise conditions.

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.