LAUSR

By considering one of the particles as a memory in a two-particle system, the entropic uncertainty relation can be improved and it is called quantum-memory-assisted entropic uncertainty relation. On the other hand, quantum coherence is an important physical resource for quantum tasks. In this work, we explore quantum-memory-assisted entropic uncertainty bound and quantum coherence for an arbitrary two-qubit X-state, and then we get analytically an explicit relation between them. As analytical examples, we consider five simple cases in which we examine the relationship between the uncertainty bound and quantum coherence. Accordingly, our results reveal that the relationship between them depends on the diagonal elements of density matrix in an arbitrary two-qubit X-state. Besides, as a numerical example, we consider a two-qubit Heisenberg XYZ model in the thermal regime and analyze the relationship between the uncertainty bound and quantum coherence.