Optimal Universal Uncertainty Relations

Tao Li, Yunlong Xiao, Teng Ma, Shao-Ming Fei, Xianqing Li-Jost, Naihuan Jing, and Zhi-Xi Wang

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Submission date: 04. Jan. 2017
Pages: 10
published in: Scientific Reports, 6 (2016), art-no. 35735 
DOI number (of the published article): 10.1038/srep35735
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Abstract:
We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89, 052115 (2014)].