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Exploring uncertainty relation and its connection with coherence under the Heisenberg spin model with the Dzyaloshinskii–Moriya interaction

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Abstract

Uncertainty principle is at the heart of quantum physics, taking a fundamental and crucial role in the area of quantum information science, and it provides a remarkable lower bound to quantify our prediction for the measured outcome of two incompatible observables. Herein, the relationship between the lower bound of the measured uncertainty and quantum coherence is investigated under a one-dimensional Heisenberg XXZ spin model with Dzyaloshinskii–Moriya (DM) interactions, and the effect of DM interaction on the entropic uncertainty is also examined in details. We reveal the systematic temperature can give rise to the increase in the measurement uncertainty of interest at thermal equilibrium. By contrast, the stronger coupling strength \( \left| J \right| \) or the stronger DM interaction would induce the decrease in the amount with respect to the uncertainty. Moreover, we analyze the dynamical behaviors of quantum coherence and find that the bound of the uncertainty is oppositely correlated with the quantum coherence dramatically. Further, the effects of DM interaction along x-direction (characterized by the parameter Dx) and z-direction (characterized by Dz) on the uncertainty of interest are discussed, respectively. For the antiferromagnetic frame J > 0, it is interesting to obtain that x-direction DM interaction Dx exhibits a more powerful influence on reducing the uncertainty and enhancing the systematic coherence, when comparing with that of Dz. With these in mind, we wish our investigations would better understand the dynamical features of the measured uncertainty in the spin-based solid systems.

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Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 61601002 and 11575001, Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), the Key Research Foundation of Education Ministry of Anhui Province of China (Grant No. KJ2015A041) and the fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

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Authors and Affiliations

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

    Fei Ming, Dong Wang, Wei-Nan Shi, Ai-Jun Huang, Ming-Ming Du, Wen-Yang Sun & 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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Correspondence to Dong Wang.

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Ming, F., Wang, D., Shi, WN. et al. Exploring uncertainty relation and its connection with coherence under the Heisenberg spin model with the Dzyaloshinskii–Moriya interaction. Quantum Inf Process 17, 267 (2018). https://doi.org/10.1007/s11128-018-2038-z

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