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arXiv:2209.15307 · International Journal of Quantum Information

Local quantum uncertainty of a two-qubit XY Heisenberg model with different Dzyaloshinskii–Moriya couplings

Younes Moqine, Brahim Adnane, Abdelhadi Belouad, Soufiane Belhouideg, Rachid Houça

Published Feb 17, 2023• 19 citations
arXivHTMLPDF

Abstract

This study investigates the local quantum uncertainty ([Formula: see text]) of a two-qubit Heisenberg XY chain with different directions of Dzyaloshinskii–Moriya (DM) interactions. The DM interaction parameters and coupling coefficient J are demonstrated to be beneficial in managing correlation. The DM interaction’s x-axis parameter has more influence on correlation than the DM interaction’s z-axis. As a result, adjusting the direction of the DM interaction with the coupling coefficient J may produce a more efficient operation to enhance the correlation.

DOI
10.1142/s0219749923400075

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This study investigates the local quantum uncertainty ([Formula: see text]) of a two-qubit Heisenberg XY chain with different directions of Dzyaloshinskii–Moriya (DM) interactions. The DM interaction parameters and coupling coefficient J are demonstrated to be beneficial in managing correlation. The DM interaction’s x-axis parameter has more influence on correlation than the DM interaction’s z-axis. As a result, adjusting the direction of the DM interaction with the coupling coefficient J may produce a more efficient operation to enhance the correlation.
In this paper, we study the thermal entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii–Moriya (DM) couplings. We show that different DM coupling parameters have different influences on the entanglement and the critical temperature. In addition, we find that when Ji (i-component spin coupling interaction) is the largest spin coupling coefficient, Di (i-component DM interaction) is the most efficient DM control parameter, which can be obtained by adjusting the direction of DM interaction.
Abstract Quantum correlations play an important role in quantum information theory. Quantum Fisher information (QFI) via local observables and via local measurements (i.e. local QFI (LQFI)) is a fundamental concept in quantum estimation and quantum metrology. LQFI captures the quantumness of correlations in a multicomponent quantum system. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In this work we will study the LQFI and the LQU in the two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction in the z -direction. Here we show that the DM interaction and spin interactions along the x - and z -axes can increase and maintain LQFI and LQU. It is also shown that because of thermal fluctuations LQFI and LQU are decreased by increasing temperature. They are equal to one at very low temperature and start to decay only after a thereshold temperature.
Abstract In this article, we investigate the dynamics and correlations of quantum-memory-assisted entropic uncertainty, the tightness of the uncertainty, entanglement, quantum correlation and mixedness for various spin chain models with Dzyaloshinskii–Moriya (DM) interaction, including the XXZ model with DM interaction, the XY model with DM interaction and the Ising model with DM interaction. We find that the uncertainty grows to a stable value with growing temperature but reduces as the coupling coefficient, anisotropy parameter and DM values increase. It is found that the entropic uncertainty is closely correlated with the mixedness of the system. The increasing quantum correlation can result in a decrease in the uncertainty, and the robustness of quantum correlation is better than entanglement since entanglement means sudden birth and death. The tightness of the uncertainty drops to zero, apart from slight volatility as various parameters increase. Furthermore, we propose an effective approach to steering the uncertainty by weak measurement reversal.
Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.
Abstract Recently, Ming et al (Quantum Inf Process 17 267, 2018) have investigated the entropic uncertainty relation in the presence of quantum memory (EUR-QM) and quantum coherence in a thermal regime for a two-spin chain under the effect of Dzyaloshinskii–Moriya (DM) interaction. Here, we study thermal quantum coherence and EUR-QM for a three-spin chain in Ising model under the effect of different directions of DM interaction. Our results confirm the results for the two-qubit case. Increasing temperature can reduce the quantum coherence but oppositely the uncertainty will grow. We show that the coupling parameter and DM interaction have constructive effects on quantum coherence and they reduce uncertainty in measurement results of incompatible observables, and especially the y -direction of DM interaction has a better influence on decreasing the uncertainty than the x and z directions. Unfortunately, the effect of the third spin acts destructively on the uncertainty and its bound, as well as the quantum coherence between the first two spins. Notably, an explicit relationship between quantum coherence and the uncertainty lower bound is found.