title: Optimal Universal Uncertainty Relations.
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)].
authors: School of Science, Beijing Technology and Business University, Beijing 100048, China.
authors: Tao
authors: T
authors: Li
authors: School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China.|Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany.
authors: Yunlong
authors: Y
authors: Xiao
authors: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.
authors: Teng
authors: T
authors: Ma
authors: Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany.|School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.
authors: Shao-Ming
authors: SM
authors: Fei
authors: School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China.|Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany.|Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.
authors: Naihuan
authors: N
authors: Jing
authors: Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany.
authors: Xianqing
authors: X
authors: Li-Jost
authors: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China.
authors: Zhi-Xi
authors: ZX
authors: Wang