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The norms of Bloch vectors and a trade-off relation of Svetlichny inequalities

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Abstract

We investigate the norms of Bloch vectors in four-partite quantum systems. An upper bound for the sum of the norms of three-order Bloch vectors has been obtained. We then present a trade-off relation of the Svetlichny inequality for any multipartite qubits systems by the upper bound. We show that for four-qubit systems, the reduced triple qubits cannot reach the maximal violate value simultaneously, while for any six-qubit state, the reduced triple qubits cannot violate Svetlichny inequality in the same time.

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Acknowledgements

This work is supported by the NSFC Nos. 11775306 and 11701568; the Fundamental Research Funds for the Central Universities Grant Nos. 16CX02049A, 17CX02033A and 18CX02023A; the Shandong Provincial Natural Science Foundation Nos. ZR2016AQ06 and ZR2017BA019

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Zong Wang, Jiahuan Qiao, Jing Wang, Ming Li & Shuqian Shen

  2. Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Ming Li

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  1. Zong Wang
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  2. Jiahuan Qiao
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  3. Jing Wang
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  4. Ming Li
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  5. Shuqian Shen
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Correspondence to Ming Li.

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Wang, Z., Qiao, J., Wang, J. et al. The norms of Bloch vectors and a trade-off relation of Svetlichny inequalities. Quantum Inf Process 17, 220 (2018). https://doi.org/10.1007/s11128-018-1990-y

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  • DOI: https://doi.org/10.1007/s11128-018-1990-y

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