Tightening the entropic uncertainty relations for multiple measurements and applying it to quantum coherence

TL;DR

This paper develops a method to tighten entropic uncertainty bounds for multiple quantum measurements, especially considering quantum memory, and applies it to quantum coherence analysis.

Contribution

It introduces a novel method to convert and tighten entropic uncertainty relations with quantum memory and applies it to multiple measurements and quantum coherence.

Findings

Tighter lower bounds for entropic uncertainty relations achieved.

Method effectively incorporates quantum memory into uncertainty bounds.

Application to quantum coherence provides new bounds on relative entropies.

Abstract

The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is expressed in terms of the entropic measures. Uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this work, we provide a method for converting the entropic uncertainty relation in the absence of quantum memory to that in its presence. It is shown that the lower bounds obtained through the method are tighter than those having been achieved so far. The method is also used to obtain the uncertainty relations for multiple measurements in the presence of quantum memory. Also for a given state, the lower bounds on the sum of the relative entropies of unilateral coherences are provided using the uncertainty relations in the presence of quantum memory, and it is shown which one is tighter.