From a single-system game to robust violations of the Bell's inequality

Abstract

Recently, Fan et al. [Mod. Phys. Lett. A 36, 2150223 (2021)], presented a generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, to identify N -qubit Greenberger-Horne-Zeilinger (GHZ) states. They showed an interesting phenomenon that the maximal violation of the generalized CHSH inequality is robust under some specific noises. In this work, we map the inequality to the CHSH game, and consequently to the CHSH* game in a single-qubit system. This mapping provides an explanation for the robust violations in N -qubit systems. Namely, the robust violations, resulting from the degeneracy of the generalized CHSH operators corresponds to the symmetry of the maximally entangled two-qubit states and the identity transformation in the single-qubit game. This explanation enables us to exactly demonstrate that the degeneracy is 2 N −2 .

Quantum cloning of steering

“…The quantum steering in the two clones are found to be bounded by an inequality, derived from the optimal fidelities of the two copied assemblages. Here, we measure the quantum steering by using the average length of steered Bloch vectors [30], which is 1/2 on the steerable boundary for the two-qubit states appearing in the process [31].…”