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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. [ABSTRACT FROM AUTHOR]

A family of steering inequalities are constructed from the chained Bell inequalities in a systematic manner. Then, with the Werner state, the Einstein–Podolsky–Rosen steering is compared with the Bell nonlocality through the comparison between the steering threshold value and the nonlocal threshold value of the chain inequalities. In particular, the difference between them becomes larger as the number of local measurement settings increases. [ABSTRACT FROM AUTHOR]

It is known that the linear n-setting steering inequalities introduced in [D. J. Saunders, S. J. Jones, H. M. Wiseman and G. J. Pryde, Nat. Phys.6 (2010) 845.] are very efficient inequalities in detecting steerability of the Werner states by using optimal measurement axes. Here, we construct chained steering inequalities that have improved visibility for the Werner states under a finite number of settings. Specifically, the threshold values of quantum violation of our inequalities for the n=4,6,10 settings are lower than those of the linear steering inequalities. Furthermore, for almost all generalized Werner states, the chained steering inequalities always have improved visibility in comparison with the linear steering inequalities. [ABSTRACT FROM AUTHOR]