Entropic uncertainty relations in the spin-1 Heisenberg model
Entropic uncertainty relations in the spin-1 Heisenberg model
复制标题
spin-1 海森堡模型中的熵不确定性关系
DOI：
10.1007/s11128-019-2196-7
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发表时间：
2019-01
影响因子：
2.5
通讯作者：
Ye Liu
中科院分区：
文献类型：
--
作者：
Shi Wei Nan;Ming Fei;Wang Dong;Ye Liu
不确定性关系为任意两个不相容的观测值建立了测量精度的内在下限，因此被视为量子理论的支柱，与经典物理学有着显著的区别。在这项工作中，我们分别研究了均匀磁场下双量子自旋-1海森堡XYZ链和XXX链中的量子记忆辅助熵不确定性关系（QMA-EUR）。我们特别推导了在海森堡XXX和XYZ模型中泡利算子（互无偏基）和SU(3)发生器上各种不相容测量的QMA-EUR的动态演化，当spinAis被测量对象和bis在信息处理过程中作为量子存储器时。值得注意的是，在相互无偏基测量的情况下，我们发现，首先，a和b之间较大的耦合强度j会导致测量不确定度的下降；其次，熵的不确定性极大地依赖于耦合强度和外磁场，这会给暴胀带来不确定性。此外，我们揭示了在SU(3)发电机上测量的不确定度的动力学行为，并证明了不确定度的动力学与前者有细微的不同。此外，我们探讨了熵不确定性与系统纠缠（负性）之间的关系，并宣布感兴趣的熵不确定性的动力学与负性的动力学近似反相关。最后，分别用负向法揭示和分析了XXX和XYZ模型下探测系统的纠缠动力学。因此，我们的观察结果可能为理解基于测量的信息处理过程中熵不确定性的动态特征铺平道路。
The uncertainty relations build an intrinsic lower bound to the measurement precision for arbitrary two incompatible observables and hence deemed as a backbone in quantum theory, strikingly distinguishing from classical physics. In this work, we examine the quantum-memory-assisted entropic uncertainty relations (QMA-EUR) in two-qutrit spin-1 Heisenberg XYZ and XXX chains under homogeneous magnetic fields, respectively. We specifically derive the dynamical evolution of QMA-EUR for various incompatible measurements on Pauli operators (mutually unbiased bases) and SU(3) generators in the Heisenberg XXX and XYZ models when spinAis the object to be measured andBis served as quantum memory during information processing. Notably, it has been found in the case of mutual unbiased-base measurements that, firstly, the larger coupling strengthJbetweenAandBcan induce the degradation of the measurement’s uncertainty; secondly, the entropic uncertainty is extremely dependent on the coupling strength and the external magnetic field, which would bring the uncertainty on the inflation. In addition, we unveil the dynamical behaviors of the uncertainty measured on SU(3) generators, and it proves that the uncertainty’s dynamics are subtly different from those in the former. Moreover, we explore the relationship between the entropic uncertainty and the system’s entanglement (negativity) and declare that the dynamics of the entropic uncertainty of interest are approximately anti-correlated with that of negativity. At last, the entanglement’s dynamics of the probed system in the XXX and XYZ models are revealed and analyzed by means of negativity, respectively. Hence, our observations might pave the way to understand the dynamical traits of the entropic uncertainty during measurement-based information processing.
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