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)].

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Cited by in corpus (6)

• The Optimal Uncertainty Relation
• Improved quantum entropic uncertainty relations
• Uncertainties of genuinely incompatible triple measurements based on statistical distance
• Quantum information measures of the one-dimensional Robin quantum well
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Optimizing incompatible triple quantum measurements