Tightening the entropic uncertainty bound in the presence of quantum memory

TL;DR

This paper improves the entropic uncertainty bound in quantum mechanics by incorporating additional information measures, resulting in a tighter lower bound that enhances understanding of quantum correlations and information processing.

Contribution

The authors derive a new, tighter lower bound for entropic uncertainty in the presence of quantum memory, extending previous bounds by including Holevo quantity and mutual information.

Findings

The new bound is tighter than Berta et al.'s bound under certain conditions.

Examples demonstrate the improved bound's effectiveness.

Applications include bounds on entanglement of formation and distillable common randomness.

Abstract

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. Berta \emph{et al}. [\href{http://www.nature.com/doifinder/10.1038/nphys1734}{ Nature Phys. 6, 659 (2010) }] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on Holevo quantity and mutual information. We conclude that our lower bound will be tighten with respect to that of Berta \emph{et al.}, when the accessible information about measurements outcomes is less than the mutual information of the joint state. Some examples have been investigated for which our lower bound is tighter than the Berta's \emph{et al.} lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has obtained, as well as an upper bound for the regularized distillable common randomness.