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.

11 pages, 2 figures

References in corpus (7)

• Device-independent security of quantum cryptography against collective attacks
• Measure of genuine multipartite entanglement with computable lower bounds
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Extremal correlations of the tripartite no-signaling polytope
• All entangled pure states violate a single Bell's inequality
• Improved lower bounds on genuine-multipartite-entanglement concurrence
• Gisin's Theorem for Arbitrary Dimensional Multipartite States

Cited by in corpus (11)

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