Robust violation of a multipartite Bell inequality from the perspective of a single-system game

Abstract

Recently, Fan \textit{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 correspond 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 $2^{N-2}$.

arXiv comment9 pages, 2 figures

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• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• Bell nonlocality
• The Einstein-Podolsky-Rosen paradox: from concepts to applications
• Bell inequality, Bell states and maximally entangled states for n qubits
• Multi-setting Bell inequality for qudits
• Tsirelson's bound and Landauer's principle in a single-system game
• New Bell inequalities for three-qubit pure states
• Deterministic transformations of three-qubit entangled pure states

Cited by in corpus (1)

• Quantum cloning of steering