An improved bound for strong unitary uncertainty relations with refined sequence

Abstract

We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy–Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three unitary operators. Compared to the known bound introduced in Yu et al (2019 Phys. Rev. A 100 022116), the unitary uncertainty relations bound with our method is tighter, to a certain extent. Meanwhile, some examples are given in the paper to illustrate our conclusions.