We investigate the behavior of various measures of quantum coherence and quantum correlation in the spin-1/2 Heisenberg XYZ model with added Dzyaloshinsky-Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions at a thermal regime described by a Gibbs density operator. We aim to understand the restricted hierarchical classification of different quantum resources, where Bell nonlocality \(\subseteq\) quantum steering \(\subseteq\) quantum entanglement \(\subseteq\) quantum discord \(\subseteq\) quantum coherence. This hierarchy highlights the increasingly stringent conditions required as we move from quantum coherence to more specific quantum phenomena. In order to enhance quantum coherence, quantum correlation, and fidelity of teleportation, our analysis encompasses the effects of independently provided sinusoidal magnetic field control as well as DM and KSEA interactions on the considered system. The results reveal that enhancing the entanglement or quantum correlation of the channel does not always guarantee successful teleportation or even an improvement in teleportation fidelity. Thus, the relationship between teleportation fidelity and the channel’s underlying quantum properties is intricate. Our study provides valuable insights into the complex interplay of quantum coherence and correlation hierarchy, offering potential applications for quantum communication and information processing technologies.
