Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario

Abstract: The quantum uncertainty principle stands as a cornerstone and a distinctive feature of quantum mechanics, setting it apart from classical mechanics. We introduce a tripartite quantum-memory-assisted entropic uncertainty relation, and extend the relation to encompass multiple measurements conducted within multipartite systems. The related lower bounds are shown to be tighter than those formulated by Zhang et al. [Phys. Rev. A 108, 012211 (2023)]. Additionally, we present generalized quantum-memory-assisted entropic uncertainty relations (QMA-EURs) tailored for arbitrary positive-operator-valued measures (POVMs). Finally, we demonstrate the applications of our results to both the relative entropy of unilateral coherence and the quantum key distribution protocols.