A Note on the Strong Unitary Uncertainty Relations

Abstract

Uncertainty relations satisfied by the product of variances of arbitrary n oservables have attracted much attention. In a recent article [Phys. Rev.Lett.120,230402(2018)], the authors provided so called strong unitary uncertainty relations for a set of unitary matrices by using the positivity property of the Gram matrix, from which uncertainty relations satisfied by two quantum mechanical observables are obtained. W e derive the explicit uncertainty relations satisfied by n quantum mechanical observables from such Gram matrix approach. By some algebraic transformations, we show that these uncertainty relations are just the same as the ones derived from a positive semi-definite Hermitian matrix generated by the mean values of n observables in [Scientific Reports 6,31192 (2016)]. P AC Snumbers: 03.65.Bz, 89.70.+c