Strong entropic uncertainty relations for multiple measurements
Yunlong Xiao, Naihuan Jing, Shao-Ming Fei, Tao Li, Xianqing Li-Jost,, Teng Ma, Zhi-Xi Wang
TL;DR
This paper develops tighter entropic uncertainty bounds for multiple measurements in finite-dimensional quantum systems, extending to Rényi and Tsallis entropies using majorization theory.
Contribution
It introduces new admixture bounds for entropic uncertainty relations applicable to multiple measurements, improving upon existing bounds and encompassing various entropy types.
Findings
New bounds are tighter than previous ones.
Bounds are valid for Shannon, Rényi, and Tsallis entropies.
Comparative analysis shows the bounds' superiority.
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\'{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.
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