Stronger Schr\"odinger-like Uncertainty Relations

TL;DR

This paper introduces a new, stronger Schr"odinger-like uncertainty relation that better captures the incompatibility of quantum observables, surpassing previous bounds and extending to three observables.

Contribution

It presents a novel, stronger uncertainty relation and an additive relation for three incompatible observables, improving upon recent existing bounds.

Findings

Stronger Schr"odinger-like uncertainty relation derived.

Additive uncertainty relation for three observables established.

Relations outperform previous bounds by Maccone, Pati, Kechrimparis, and Weigert.

Abstract

Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger Schr\"odinger-like uncertainty relation, which is stronger than the relation recently derived by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113 (2014) 260401]. Furthermore, we give an additive uncertainty relation which holds for three incompatible observables, which is stronger than the relation newly obtained by S. Kechrimparis and S. Weigert [Phys. Rev. A 90 (2014) 062118] and the simple extension of the Schr\"odinger uncertainty relation.