Dzyaloshinskii-Moriya相互作用下Ising模型的线性熵测不准关系

doi:10.3969/j.issn.1000-5641.2024.03.016

摘要/Abstract

摘要：

以Dzyaloshinskii-Moriya (DM) 相互作用下两比特Ising模型为研究对象, 研究了耦合强度、DM相互作用和环境温度对该自旋模型中的线性熵测不准关系(entropy uncertainty relation, EUR)的影响, 同时分析了系统热纠缠随环境温度的变化, 并将热纠缠与线性熵测不准关系做了对比. 研究表明, 系统线性熵不确定度、热纠缠的变化趋势取决于环境参数的选择, 且二者整体演化行为近似反相关. 此外, 对一组完备的互无偏基在选择不同测量基组合情况下, 测不准关系的下界会随着测量基个数的不同而变化; 而且这种线性熵测不准关系在特殊条件下可化为等式, 其下界与具体观测量选取无关. 与以往量子存储辅助熵测不准关系相比, 线性熵测不准关系可为精密测量提供有益的参考.

关键词: 熵测不准关系, 热纠缠, 互无偏基

Abstract:

In this research, by considering the two-qubit Ising model under Dzyaloshinskii-Moriya(DM) interaction as the research object, we investigate the effects of coupling strength, DM interaction and ambient temperature on the linear entropy uncertainty relation(EUR) in the system. Meanwhile, the variation of thermal entanglement with environment with ambient temperature is also discussed, and the relationship between thermal entanglement and linear EUR is compared. The results demonstrate that the systemic linear entropy uncertainty and thermal entanglement variance trend depends on the selection of environmental parameters, and their overall evolution behavior is roughly anti-related. Additionally, for a complete set of mutually unbiased bases, when different measurement base combinations are selected, the uncertainty relation lower bound will vary with the change in the number of measurement bases; moreover, the linear EUR can be transformed into an equation in special cases and its lower bound does not depend on the selection of a specific observation quantity. Compared with the previous quantum memory-assisted EUR, it provides a useful reference for precise measurement.

Key words: entropy uncertainty relation, thermal entanglement, mutual unbiased bases

中图分类号:

O431

赵宇, 刘金明. Dzyaloshinskii-Moriya相互作用下Ising模型的线性熵测不准关系[J]. 华东师范大学学报（自然科学版）, 2024, 2024(3): 147-155.

Yu ZHAO, Jinming LIU. Linear entropy uncertainty relation of Ising model under Dzyaloshinskii-Moriya interaction[J]. Journal of East China Normal University(Natural Science), 2024, 2024(3): 147-155.

图/表 4

参考文献 24

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