Stronger Schrödinger-like uncertainty relations

•A stronger Schrödinger-like uncertainty relation in the sum of variances of two observables is obtained.•An improved Schrödinger-like uncertainty relation in the product of variances of two observables is obtained.•A stronger uncertainty relation in the sum of variances of three observables is proposed.

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 Schrödinger-like uncertainty relation, which is stronger than the relation recently derived by Maccone and Pati (2014) [11]. Furthermore, we give an additive uncertainty relation which holds for three incompatible observables, which is stronger than the relation newly obtained by Kechrimparis and Weigert (2014) [12] and the simple extension of the Schrödinger uncertainty relation.