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The uncertainty principle sets limit on our ability to predict the values oftwo 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 bealtered by considering a particle as a quantum memory correlating with theprimary particle. In this work, we provide a method for converting the entropicuncertainty 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 thanthose having been achieved so far. The method is also used to obtain theuncertainty relations for multiple measurements in the presence of quantummemory. Also for a given state, the lower bounds on the sum of the relativeentropies of unilateral coherences are provided using the uncertainty relationsin the presence of quantum memory, and it is shown which one is tighter.

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