Stronger variance-based unitary uncertainty relations

In this paper, we construct stronger lower bounds for the variance-based uncertainty relations of two unitary operators, via the power-mean inequalities. It is proved that these bounds are tighter in any interval, compared to the bounds given by Bong et al. (Phys Rev Lett 120:230402, 2018) and by Yu et al. (Phys Rev A 100:022116, 2019). Moreover, we build descending sequences of lower bounds for the uncertainty relations of two or three unitary operators. For illustration, some explicit examples are given to show the tightness of our bounds, in both pure and mixed state cases.