Stronger Schr\"odinger-like Uncertainty Relations

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.