A Note on the Strong Unitary Uncertainty Relations
Xiaofen Huang, Ting-Gui Zhang, Xianqing Li-Jost, Yuan-Hong Tao, and Shao-Ming Fei
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Submission date: 11. Feb. 2019
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Uncertainty relations satisﬁed by the product of variances of arbitrary n observables 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. We 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)].