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Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions

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Abstract

The dynamics of measurement’s uncertainty via entropy for a one-dimensional Heisenberg XYZ mode is examined in the presence of an inhomogeneous magnetic field and Dzyaloshinskii–Moriya (DM) interaction. It shows that the uncertainty of interest is intensively in connection with the filed’s temperature, the direction-oriented coupling strengths and the magnetic field. It turns out that the stronger coupling strengths and the smaller magnetic field would induce the smaller measurement’s uncertainty of interest within the current spin model. Interestingly, we reveal that the evolution of the uncertainty exhibits quite different dynamical behaviors in antiferromagnetic (Ji > 0) and ferromagnetic (Ji < 0) frames. Besides, an analytical solution related to the systematic entanglement (i.e., concurrence) is also derived in such a scenario. Furthermore, it is found that the DM-interaction is desirably working to diminish the magnitude of the measurement’s uncertainty in the region of high-temperature. Finally, we remarkably offer a resultful strategy to govern the entropy-based uncertainty through utilizing quantum weak measurements, being of fundamentally importance to quantum measurement estimation in the context of solid-state-based quantum information processing and computation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61601002 and 11575001), Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), and the Fund of CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

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Authors and Affiliations

  1. School of Physics & Material Science, Anhui University, Hefei, 230601, China

    Ying-Yue Yang, Wen-Yang Sun, Wei-Nan Shi, Fei Ming, Dong Wang & Liu Ye

  2. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China

    Dong Wang

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  1. Ying-Yue Yang
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Correspondence to Dong Wang.

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Yang, YY., Sun, WY., Shi, WN. et al. Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions. Front. Phys. 14, 31601 (2019). https://doi.org/10.1007/s11467-018-0880-1

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