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Quantum-Memory-Assisted Entropic Uncertainty Relation in the Heisenberg XXZ Spin Chain Model with External Magnetic Fields and Dzyaloshinski-Moriya Interaction

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Abstract

In this paper, we investigate the quantum-memory-assisted (QMA) entropic uncertainty relation in the two-qubit Heisenberg XXZ spin chain model. The contributions of relevant parameters of the model on the reducing of QMA entropic uncertainty concerning a pair of Pauli observables are studied in detail under the thermal equilibrium and intrinsic decoherence conditions, respectively. The results show that, in the case of thermal equilibrium, the lower of T and the stronger of spin coupling interaction J, Jz and Dzyaloshinskii-Moriya (DM) interaction Dz are more beneficial to the reducing of QMA entropic uncertainty. However, the stronger of external nonuniform magnetic field \(\mathfrak {B}\) hinders the reducing of the QMA entropic uncertainty. Meanwhile, there exists a critical phenomena with respect to \(\mathfrak {B}\) at the extremal low temperature. By taking into account the effect of intrinsic decoherence, it is found that the dynamical features of QMA entropic uncertainty are sensitive to the values of Dz and unnonuniform magnetic fields \(\mathfrak {b}\). In the weak DM interaction region, the strengthening of Dz can markedly reduce the entropic uncertainty U during the evolution process, but, in the strong DM interaction region, the strengthening of Dz makes the effect of intrinsic decoherence more pronounced. Furthermore, the large nonuniformity \(\mathfrak {b}\) dose not suppress the entropic uncertainty but makes the oscillation behaviours of U and Ub disappear. The large nonuniformity \(\mathfrak {b}\) also makes the effect of intrinsic decoherence more pronounced.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant No.12064012 and No.11464015, the Natural Science Foundation of Hunan Province under Grant No.2020JJ4496, the Youth Scientific Project of Education Ministry of Hunan Province under Grant No.21B0518, the Scientific Project of Jishou University under Grant No. Jd21005.

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Authors and Affiliations

  1. School of Software, Jishou University, Zhangjiajie, 427000, People’s Republic of China

    Yanliang Zhang, Qingping Zhou & Guodong Kang

  2. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Yanliang Zhang & Maofa Fang

  3. School of Physics, Jishou University, Zhangjiajie, 416000, People’s Republic of China

    Jiaxin Wen

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  1. Yanliang Zhang
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Correspondence to Yanliang Zhang.

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Zhang, Y., Zhou, Q., Kang, G. et al. Quantum-Memory-Assisted Entropic Uncertainty Relation in the Heisenberg XXZ Spin Chain Model with External Magnetic Fields and Dzyaloshinski-Moriya Interaction. Int J Theor Phys 61, 139 (2022). https://doi.org/10.1007/s10773-022-05130-w

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