Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements

TL;DR

This paper extends quantum uncertainty relations to three observables with quantum memory, deriving new bounds involving complementarity, entropies, and information measures, and analyzing conditions for equality.

Contribution

It introduces tripartite quantum memory-assisted entropic uncertainty relations with novel bounds involving multiple information-theoretic quantities.

Findings

Derived new tripartite uncertainty bounds

Analyzed conditions for saturation of inequalities

Connected bounds to complementarity and information measures

Abstract

Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum memory-assisted entropic uncertainty relations and show that the lower bounds of these relations have three terms that depend on the complementarity of the observables, the conditional von-Neumann entropies, the Holevo quantities, and the mutual information. The saturation of these inequalities is analyzed.