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Monogamy Relations of Measurement-Induced Disturbance

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Abstract

The standard monogamy imposes severe limitations to sharing quantum correlations in multipartite quantum systems, which is a star topology and is established by Coffman, Kundu and Wootters. In this work, we discuss some monogamy relations beyond it, and focus on the measurement-induced disturbance (MID) which quantifies the multipartite quantum correlation. We prove exactly that MID obeys the property of discarding quantum systems never increases in an arbitrary quantum state. Moreover, we define a new kind of sharper monogamy relation which shows that the sum of all bipartite MID can not exceed the amount of total MID. This restriction is similarly called a mesh monogamy. We numerically study how MID is distributed in a 4-qubit mixed state, and which relation exists between the mesh monogamy of MID and the level of obeying the standard monogamy.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11401347, 61202317, 61572246, 61602232), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015FQ006), the Plan for Scientific Innovation Talents of Henan Province(Grant No. 164100510003), and the Key Scientific Project in Universities of Henan Province (Grant No. 16A520021).

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Authors and Affiliations

  1. College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, 264005, China

    Feng Liu & Yun-Xia Wei

  2. Key Laboratory of Information Security, School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Fei Li

  3. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, China

    Fei Li

  4. School of Science, Qingdao Technological University, Qingdao, 266033, China

    Hong-Yang Ma

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  1. Feng Liu
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  2. Fei Li
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  3. Yun-Xia Wei
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Correspondence to Feng Liu.

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Liu, F., Li, F., Wei, YX. et al. Monogamy Relations of Measurement-Induced Disturbance. Int J Theor Phys 56, 1903–1911 (2017). https://doi.org/10.1007/s10773-017-3336-4

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  • DOI: https://doi.org/10.1007/s10773-017-3336-4

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