Strong entropic uncertainty relations for multiple measurements
Abstract
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\'enyi and Tsallis entropies besides the Shannon entropy. We employ majorization theory and actions of the symmetric group to obtain an admixture bound for entropic uncertainty relations for multi-measurements. Comparisons among all bounds for multi-measurements are shown in figures in our favor.
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