Entropic uncertainty relations with quantum memory in a multipartite scenario

TL;DR

This paper introduces two new multipartite entropic uncertainty relations with quantum memory, providing tighter bounds that enhance understanding of quantum measurement uncertainties in complex systems.

Contribution

It generalizes previous relations to multipartite scenarios and derives bounds dependent on complementarity, entropies, and mutual information.

Findings

New bounds are tighter than previous ones.

Bounds depend on observable complementarity and information measures.

Illustrations show improved performance in typical cases.

Abstract

Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$ [Phys Rev A. 106. 062219 (2022)]. Interestingly, the quantum-memory-assisted entropic uncertainty relation for multiple measurement settings can be further generalized. In this work, we propose two complementary multipartite quantum-memory-assisted entropic uncertainty relations and our lower bounds depend on values of complementarity of the observables, (conditional) von-Neumann entropies, Holevo quantities, and mutual information. As an illustration, we provide several typical cases to exhibit that our bounds are tighter and outperform the previous bounds.