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Laser Physics Letters

Nonlocal advantage of quantum coherence in the spin-1/2 and spin-1 Heisenberg XXZ models

Yu-Xia Xie, Yuhan Zhang

Published Feb 5, 2020• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ab6aa4

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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.
Abstract Quantum correlations in a state can be quantified from different aspects. The nonlocal advantage of quantum coherence (NAQC) captures quantum correlation stronger than entanglement and Bell nonlocality. We investigate the NAQC-type quantum correlation in the Heisenberg XY model and showed that both the anisotropy of the interaction between two spins and the external transverse magnetic field can serve as efficient parameters for tuning the NAQC-type quantum correlation. In particular, for the relative low temperature case there is a finite parameter region in which the strength of the NAQC-type quantum correlation is of about its maximum 1. We also found there are quantum states for which the NAQC-type quantum correlations defined by the l 1 norm of coherence and the relative entropy of coherence have a different ordering.
Abstract Average steered coherence (ASC) reflects the nonlocal property of a state from a fundamental aspect and the steerable states achieve a nonlocal advantage of quantum coherence (NAQC) when the ASC exceeds a threshold. We explore the ASC in both the spin-1 XXZ model with Dzyaloshinskii–Moriya (DM) and Kaplan–Shekhtman-Entin–Wohlman–Aharony (KSEA) interactions and the dimerized XXZ model. For the first model, it is found that the ASC in the thermal state can be enhanced by tuning the anisotropic parameter and the DM and KSEA interactions; while for the second model, the ASC can be enhanced by tuning the J 2 interaction and there exists a temperature plateau at which it remains almost the constant. Besides, for both the spin-1 models, a NAQC can always be achieved by optimizing the involved controlling parameters.
Abstract Quantum coherence is not only a fundamental notion in quantum theory but also an invaluable resource for quantum information processing. We investigate the nonlocal advantage of quantum coherence (NAQC) in the Heisenberg model, aimed at seeking flexible ways for its control. By considering impurities, or more explicitly, the inhomogeneous spin couplings and nonuniform magnetic field, in such a model, we showed that an efficient nonlocal control of the NAQC can be realized, and there exists a wide impurity parameter region for which the NAQC takes the value a little less than its maximum 1. Moreover, the critical temperature after which the NAQC vanishes can also be enhanced evidently by tuning the impurity parameters.
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.
Abstract We investigate the nonlocal advantage of quantum coherence (NAQC) for two qubits coupled via the Heisenberg interaction and embedded in their respective thermal and dephasing reservoirs. Unlike the case of two uncoupled qubits, we showed that in the presence of the Heisenberg interaction, the decay rate of the NAQC can be reduced and the strength of the NAQC can be enhanced for certain initial states. Moreover, the Heisenberg interaction of two spins can induce generation of NAQC from the initial product states, and the generated NAQC approaches asymptotically to its maximum with the increasing anisotropy of the Heisenberg interaction.
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.