Strong entropic uncertainty relations for multiple measurements

In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R'{e}nyi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an {\it admixture bound} for entropic uncertainty relations for multi-measurements. Comparisons among all bounds for multi-measurements are shown in figures in our favor.