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Laser Physics Letters

Characterizing quantum nonlocalities under the Heisenberg XYZ spin model with Dzyaloshinskii–Moriya interaction

Ling-Ling Xing, Huan Yang, Zong Xu, Xun-Mei Hu, Ze-Bin Li, Min Kong, Gang Zhang

Published Jun 30, 2022• 0 citations
Publisher

Abstract

Abstract In quantum information science, the nontrivial applications of the Heisenberg spin model are to realize quantum communication and quantum computing using the quantum nonlocalities between particles in the spin chain. Here, considering Heisenberg XYZ spin model with Dzyaloshinskii–Moriya (DM) interaction, our attentions are directed to ascertain the nonlocal advantage of quantum coherence (NAQC), and also characterize the Bell nonlocality (BN). As revealed from the results, one can use low temperature to realize situations in which the NAQC and BN are invariant. The NAQC and BN cannot be detected if temperature is high. External temperature strongly influences the two quantum nonlocalities in ferromagnetic systems. The strong coupling parameter ℑ x brings on the fact that the two quantum nonlocalities are invariant. It is very difficult to capture the NAQC and BN if ℑ x is weak. Considering ℑ y > 0 , the strong ℑ y is responsible for freezing quantum nonlocalities, and one cannot witness the NAQC when ℑ y is low. Moreover, the freezing of quantum nonlocalities can be achieved via enhancing ℑ z , and the detection of NAQC is difficult if ℑ z is weak. Of particular note, under the influence of DM interactions, NAQC (BN) cannot (can) be frozen both in antiferromagnetic and ferromagnetic systems. The strong D y and D z give rise to the difficulty of capturing the NAQC.

DOI
10.1088/1612-202x/ac73fc

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Abstract The non-local advantage of quantum coherence (NAQC) is regarded as a quantum correlation, which can be reflected by the violation of a set of inequalities based on various coherence measures. In this work, we explore the NAQC and Bell nonlocality (BN) in a two-qubit Heisenberg XYZ model. The results show that one can capture the BN in the case of both anti-ferromagnetism and ferromagnetism. By contrast, the NAQC cannot be achieved in the ferromagnetism case if the magnetic field is strong. Increases of inhomogeneity and temperature give rise to reductions of the NAQC and BN, and the achievement of the NAQC at high inhomogeneity or temperatures becomes very difficult. Also, the NAQC and BN strengthen with an increase of the mean coupling coefficient. A strong mean coupling coefficient leads to the freezing of the NAQC and BN when the inhomogeneity is low. The enhancement of the magnetic field can result in the fact that the NAQC and BN experience four processes, including reduction, sudden death, revival, and reduction. Additionally, the BN is easier to capture than the NAQC. Furthermore, we focus our attention on controlling the NAQC and BN via a local filtering operation. The results demonstrate that the operation can effectively strengthen the NAQC and BN, and can also help us to control the NAQC and BN in the Heisenberg XYZ chain.
We investigate the quantum correlations of a two-qubit XYZ Heisenberg spin-1/2 chain model with Dzyaloshinskii–Moriya interaction. The two-qubit system is considered in thermal equilibrium. The variations of logarithmic negativity, uncertainty-induced quantum nonlocality (UIN) and trace distance discord, versus the parameters characterizing the system, are analyzed. The results show that the UIN measure captures quantum correlations that cannot be revealed by entanglement and trace discord. We also show that the Dzyaloshinskii–Moriya interaction enhances the non-classical correlations between the spins and can weaken the undesirable destructive effects of thermal fluctuations. In addition, an entangled–unentangled phase transition can be detected from the behavior of logarithmic negativity.
Abstract Quantum coherence underlies different forms of quantum correlations. We investigate the nonlocal advantage of quantum coherence (NAQC) for the thermal equilibrium states of both the spin-1/2 and the spin-1 Heisenberg XXZ models. By considering the NAQC formulated within two slightly different frameworks, we showed that their values can always be enhanced by tuning strength of the spin-exchange interaction along the z direction. The maximum achievable NAQC by tuning decreases with the increasing temperature T and there will be no NAQC when T is higher than a critical value. Moreover, both the NAQC and the critical temperature could be further noticeably increased by introducing the Dzyaloshinsky–Moriya interaction along either the z direction or the x direction to the considered spin models.
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In this paper, we explore nonlocal correlation and Bell non-locality in a two-qubit Heisenberg XYZ model by using Bell-CHSH inequality and uncertainty induced nonlocality (UIN) as well as log-negativity. We consider the effects of spin-qubits XYZ-Heisenberg couplings, the y-component of DM interaction, and intrinsic decoherence. Our results show that spin-qubits Heisenberg couplings have a strong ability to create two-qubit nonlocal correlations, enhanced by combining with DM interactions. The generated Bell-CHSH nonlocality and entanglement conform to the hierarchy principle. The UIN correlation is more resistant to intrinsic decoherence compared to Bell-CHSH inequality and log-negativity. Intrinsic decoherence causes the disappearance of Bell-CHSH non-locality and log-negativity entanglement, while leading to the appearance of partial stationary spin-qubits UIN correlation.
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