Weighted Uncertainty Relations

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

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Submission date: 07. Jul. 2016
Pages: 12
published in: Scientific Reports, 6 (2016), art-no. 23201 
DOI number (of the published article): 10.1038/srep23201
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Abstract:
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.