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Strong entropic uncertainty relations for multiple measurements
Yunlong Xiao, Naihuan Jing, Shao-Ming Fei, Tao Li, Xianqing Li-Jost, Teng Ma and Zhi-Xi Wang
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 Renyi 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 given in two figures.