MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Weighted Uncertainty Relations

Yunlong Xiao, Naihuan Jing, Xianqing Li-Jost and Shao-Ming Fei


Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation.

Jul 7, 2016
Jul 14, 2016

Related publications

2016 Journal Open Access
Yunlong Xiao, Nai-Huan Jing, Xianqing Li-Jost and Shao-Ming Fei

Weighted uncertainty relations

In: Scientific reports, 6 (2016), p. 23201