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Exploring the nonlocal advantage of quantum coherence and Bell nonlocality in the Heisenberg XYZ chain

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.