Tight upper bound for the maximal expectation value of the Mermin operators

Abstract

The violation of the Mermin inequality (MI) for multipartite quantum states guarantees the existence of nonlocality between either few or all parties. The detection of optimal MI violation is fundamentally important, but current methods only involve numerical optimizations, thus hard to find even for three-qubit states. In this paper, we provide a simple and elegant analytical method to achieve the upper bound of Mermin operator for arbitrary three-qubit states. Also, the necessary and sufficient conditions for the tightness of the bound for some class of tri-partite states has been stated. Finally, we suggest an extension of this result for up to n qubits.

8 pages, 1 figure, revised version, accepted in Quantum Information Processing

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Cited by in corpus (6)

• Entropy bounds for multiparty device-independent cryptography
• Revisiting the experimental test of Mermin's inequalities at IBMQ
• 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
• Mermin and Svetlichny inequalities for non-projective measurement observables
• Revealing hidden standard tripartite nonlocality by local filtering