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 optimization, thus hard to find even for three qubit states. In this paper, we provide a simple and elegant analytical method to achieve the tighter 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 states has been stated.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 optimization, thus hard to find even for three qubit states. In this paper, we provide a simple and elegant analytical method to achieve the tighter 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 states has been stated.

Oct 30, 20170 citations

New variational bounds on expectation values

Michael Fielding Barnsley, Peter D. Robinson

Oct 1, 19750 citations

Tight Upper Bound for the Maximal Expectation Value of the N $N$ ‐Partite Generalized Svetlichny OperatorTight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

Youwang Xiao, Zong Wang, Wen‐Na Zhao +1 more

Abstract Genuine multipartite non‐locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The ‐partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary ‐qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger‐Horne‐Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non‐locality and can potentially be applied to other quantum information processing tasks.Abstract Genuine multipartite non‐locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The ‐partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary ‐qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger‐Horne‐Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non‐locality and can potentially be applied to other quantum information processing tasks.

arXiv:2409.08490Advanced Quantum TechnologiesApr 21, 20243 citations

EXPECTATION VALUES OF OPERATORS

WORLD SCIENTIFIC eBooksJun 23, 20131 citation

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

Ming Li, Shu‐Qian Shen, Naihuan Jing +2 more

It is a challenging task to detect genuine multipartite nonlocality (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 inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (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 of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.It is a challenging task to detect genuine multipartite nonlocality (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 inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (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 of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.

arXiv:1710.01601Physical Review AOct 16, 201722 citations

Tight Upper Bound for the Maximal Expectation Value of the N

N

‐Partite Generalized Svetlichny Operator