Nonlocality is an important resource for quantum information processing. Genuine tripartite nonlocality, which is sufficiently confirmed by the violation of Svetlichny inequality, is a kind of more precious resource than the standard one. The genuine tripartite nonlocality is usually quantified by the amount of maximal violation of Svetlichny inequality. The problem of detecting and quantifying the genuine tripartite nonlocality of quantum states is of practical significance but still open for the case of general three-qubit quantum states. In this paper, we quantitatively investigate the genuine nonlocality of three-qubit states, which not only include pure states but also include mixed states. Firstly, we derive a simplified formula for the genuine nonlocality of a general three-qubit state, which is a function of the corresponding three correlation matrices. Secondly, we develop three properties of the genuine nonlocality which can help us to analyze the genuine nonlocality of complex states and understand the nature of quantum nonlocality. Further, we get analytical results of genuine nonlocality for two classes of three-qubit states which have special correlation matrices. In particular, the genuine nonlocality of generalized three-qubit GHZ states, which is derived by Ghose et al. (Phys. Rev. Lett. 102, 250404, 2009), and that of three-qubit GHZ-symmetric states, which is derived by Paul et al. (Phys. Rev. A 94, 032101, 2016), can be easily derived by applying the strategy and properties developed in this paper.
Quantum information Tripartite nonlocality Svetlichny inequality
This is a preview of subscription content, log in to check access.
The author is delighted to thank Professor Yuan Feng for illuminating and fruitful discussions in the last four years which helps Zhaofeng to lay solid foundations for further research. This research is partially supported by National Key R&D Program of China (Grant No. 2016YFB0200602), Chinese Scholarship Council (Grant No. 201206270069), Australian Research Council (Grant No. DP160101652) and National Natural Science Foundation of China (Grant Nos. 61472452 and 61772565).
Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)ADSCrossRefzbMATHGoogle Scholar
Horodecki, R., Horocecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-1/2 states: necessary and sufficient condition. Phys. Lett. A 200, 340–344 (1995)ADSMathSciNetCrossRefzbMATHGoogle Scholar