Optimal Universal Uncertainty Relations

TL;DR

This paper introduces a new method called joint probability distribution diagram to improve universal uncertainty relations, providing tighter bounds and complementing existing entropic uncertainty relations.

Contribution

It presents a novel approach to majorization bounds for uncertainty relations, enhancing their state-independent applicability and offering a complementary perspective to recent entropic results.

Findings

Improved majorization bounds for uncertainty relations

State-independent uncertainty relations for Schur-concave functions

Complementary bounds to recent entropic 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)].