Abstract:

In this research, by considering the two-qubit Ising model under Dzyaloshinskii-Moriya(DM) interaction as the research object, we investigate the effects of coupling strength, DM interaction and ambient temperature on the linear entropy uncertainty relation(EUR) in the system. Meanwhile, the variation of thermal entanglement with environment with ambient temperature is also discussed, and the relationship between thermal entanglement and linear EUR is compared. The results demonstrate that the systemic linear entropy uncertainty and thermal entanglement variance trend depends on the selection of environmental parameters, and their overall evolution behavior is roughly anti-related. Additionally, for a complete set of mutually unbiased bases, when different measurement base combinations are selected, the uncertainty relation lower bound will vary with the change in the number of measurement bases; moreover, the linear EUR can be transformed into an equation in special cases and its lower bound does not depend on the selection of a specific observation quantity. Compared with the previous quantum memory-assisted EUR, it provides a useful reference for precise measurement.

Key words: entropy uncertainty relation, thermal entanglement, mutual unbiased bases