Tight bounds from multiple-observable entropic uncertainty relations

TL;DR

This paper explores entropic uncertainty relations in quantum systems, revealing how their additivity properties depend on the number of observables and linking violations to quantum correlations.

Contribution

It introduces new state-independent and state-dependent entropic inequalities and analyzes their additivity properties in bipartite and multipartite systems.

Findings

Additivity holds only for two-observable EURs.

Violations of inequalities indicate quantum correlations.

Additivity does not extend to inequalities with more than two observables.

Abstract

We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular, we introduce state-independent and state-dependent entropic inequalities. Interestingly, the violation of these inequalities is strictly connected with the presence of quantum correlations. We show that the additivity of EUR holds only for EUR that involve two observables, while this is not the case for inequalities that consider more than two observables or the addition of the von Neumann entropy of a subsystem. We apply them to bipartite systems and to several classes of states of a three-qubit system.