Tight upper bound for the maximal quantum value of the Svetlichny operators

Abstract

It is a challenging task to detect genuine multipartite nolocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequalities (SI) for several quantum states, including the white and color noised GHZ states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation on GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.

arXiv comment11 pages, 2 figures

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• Interplay of nonlocality and incompatibility breaking qubit channels
• Tight upper bound on the quantum value of Svetlichny operators under local filtering and hidden genuine nonlocality
• Verifying Hierarchic Multipartite and Network Nonlocalities with a Unified Method
• Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems
• Tight upper bound for the maximal expectation value of the $N$-partite generalized Svetlichny operator
• Distribution of spin correlation strengths in multipartite systems
• Strength of the nonlocality of two-qubit entangled state and its applications
• Mermin and Svetlichny inequalities for non-projective measurement observables
• Revealing hidden standard tripartite nonlocality by local filtering
• Quantum Zeno Effect on Genuine Tripartite Nonlocality and Entanglement in Quantum Dissipative System