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Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions |
Ying-Yue Yang1, Wen-Yang Sun1, Wei-Nan Shi1, Fei Ming1, Dong Wang1,2(), Liu Ye1 |
1. School of Physics & Material Science, Anhui University, Hefei 230601, China 2. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China |
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Abstract The dynamics of measurement’s uncertainty via entropy for a one-dimensional Heisenberg XY Z 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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Keywords
measurement uncertainty
concurrence
Heisenberg XY Z chain
weak measurement
lower bound
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Corresponding Author(s):
Dong Wang
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Issue Date: 30 January 2019
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