Characterizing multipartite entanglement by violation of CHSH inequalities
Ming Li, Hui-Hui Qin, Chengjie Zhang, Shu-Qian Shen, Shao-Ming Fei, and Heng Fan
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Submission date: 17. Mar. 2020
published in: Quantum information processing, 19 (2020) 5, art-no. 142
DOI number (of the published article): 10.1007/s11128-020-02638-0
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Entanglement of high-dimensional and multipartite quantum systems offer promising 3 perspectives in quantum information processing. However, the characterization and 4 measure of such kind of entanglement is of great challenge. Here, we consider the 5 overlaps between the maximal quantum mean values and the classical bound of the 6 CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show 7 that the concurrence of a pure state in any high-dimensional multipartite system can 8 be equivalently represented by these overlaps. Here, we consider the projections of 9 an arbitrary high-dimensional multipartite state to two-qubit states. We investigate 1 10 the non-localities of these projected two-qubit sub-states by their violations of CHSH 11 inequalities. From these violations, the overlaps between the maximal quantum mean 12 values and the classical bound of the CHSH inequality, we show that the concurrence 13 of a high-dimensional multipartite pure state can be exactly expressed by these over- 14 laps. We further derive a lower bound of the concurrence for any quantum states, 15 which is tight for pure states. The lower bound not only imposes restriction on the 16 non-locality distributions among the pairwise-qubit states, but also supplies a sufficient 17 condition for distillation of bipartite entanglement. Effective criteria for detecting gen- 2 18 uine tripartite entanglement and the lower bound of concurrence for genuine tripartite 19 entanglement are also presented based on such non-localities.