Tripartite quantum-memory-assisted entropic uncertainty relations in three-qubit Heisenberg XXZ spin model with DM and KASE interactions

In this paper, we have investigated the dynamical features of tripartite quantum-memory-assisted entropic uncertainty (tQMA-EU) and its two corresponding lower bounds in three-qubit Heisenberg XXZ spin chain model with Dzyaloshinskii-Moriya (DM) interaction and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction. The results show that, when the DM and KSEA interaction are taken account, the Dolatkhah's lower bound is always equal to the tQMA-EU and remains higher than the Ming's lower bound in both ferromagnetic and antiferromagnetic cases.The increasing of DM and KASE interactions can effectively reduce the value of tQMA-EU, the varying behaviors of tQMA-EU with respect to DM and KASE interactions from positive and negative intervals demonstrate central symmetry. Particularly, in ferromagnetic case, this reduction effect is more pronounced than that in antiferromagnetic case. In addition, the dynamical features of Dolatkhah's lower bound and Ming's lower bound with respect to the spin chain systemic parameters display distinct differences in the ferromagnetic and antiferromagnetic cases. Specifically, in the ferromagnetic case and with weak DM interaction, during the lower temperature range, under the influence of the KSEA interaction and under an external magnetic field, the Dolatkhah's lower bound dosen't negative-correlated to tripartite negativity quantum correlation N _ABC . in contrast, the dynamics of Ming's lower bound show negative-correlated to N _ABC .