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.
Quantum steering ellipsoid (QSE) can faithfully characterize arbitrary bipartite state, and provide a new method to visually investigate and capture various quantum nonlocalities. Note that the dissipation of quantum nonlocalities can be accelerated by the coupling between the system and the decoherence channel, which induces great challenges in detecting quantum nonlocalities. Herein, considering the scenario in which the subsystem of a two-qubit system is coupled with a decoherence channel, the quantum discord (QD) and concurrence are visually characterized and detected by employing the QSE. The results reveal that the QSE y and z semiaxes are responsible for the traits of the QD and concurrence under the bit flip channel. The x and y semiaxes dominate and visualize the QD and concurrence under the phase damping channel. Of particular note is that one can realize the detections of the QD and concurrence via the shape of the QSE. To be clearer, the disappearance of the QD can be ascertained according to a needle-shaped QSE or a vanishing QSE in the Bloch sphere. In contrast, one can witness the concurrence if the total semiaxis length is greater than one. Beyond this, our results visually reveal that quantum entanglement is a stronger quantum nonlocality than the QD from the perspective of geometry, and thus deepens the understanding of the quantum nonlocality.
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