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

TL;DR

This paper develops tighter entropic uncertainty relations with quantum memory for multipartite systems, extending previous bounds and applying to various measurement types, with implications for quantum coherence and key distribution.

Contribution

It introduces a tripartite quantum-memory-assisted entropic uncertainty relation and extends it to multiple measurements and POVMs, improving existing bounds.

Findings

Tighter lower bounds than previous relations.

Extension to multiple measurements in multipartite systems.

Applications to quantum coherence and quantum key distribution.

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.