Trade-off Relations of Bell Violations among Pairwise Qubit Systems
Hui-Hui Qin, Shao-Ming Fei, and Xianqing Li-Jost
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Submission date: 20. Jan. 2016
published in: Physical review / A, 92 (2015) 6, art-no. 062339
DOI number (of the published article): 10.1103/PhysRevA.92.062339
PACS-Numbers: 03.67.Mn, 03.67.-a, 02.20.Hj, 03.65.-w
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We investigate the non-locality distributions among multi-qubit systems based on the maximal violations of the CHSH inequality of the reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of non-locality among the sub-qubit systems. For a three-qubit system, it is impossible that all pair of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to display the trade-off relations, and the trade-off relations are generalized to arbitrary multi-qubit systems.