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arXiv · 1911.07699

Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems

Li-Jun Zhao·Lin Chen·Yu-Min Guo·Kai Wang·Yi Shen·Shao-Ming Fei
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Abstract

We study the trade-off relations satisfied by the genuine tripartite nonlocality in multipartite quantum systems. From the reduced three-qubit density matrices of the four-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states and W states (4-qubit entangled state), we find that there exists a trade-off relation among the mean values of the Svetlichny operators associated with these reduced states. Namely, the genuine three-qubit nonlocalities are not independent. For four-qubit generalized GHZ states and W states, the summation of all their three-qubit maximal (squared) mean values of the Svetlichny operator has an upper bound. This bound is better than the one derived from the upper bounds of individual three-qubit mean values of the Svetlichny operator. Detailed examples are presented to illustrate the trade-off relation among the three-qubit nonlocalities.

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Li-Jun Zhao, Lin Chen, Yu-Min Guo, Kai Wang, Yi Shen, Shao-Ming Fei. 2019-11-18. Trade-off relation among genuine three-qubit nonlocalities in four-qubit systems. https://doi.org/10.1103/physreva.100.052107

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