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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 (www.arxiv.org) 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
20/2017

Strong Variance-Based Uncertainty Relations and Uncertainty Intervals

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

Abstract

Uncertainty relations occupy a fundamental position in quantum mechanics. We propose stronger variance-based uncertainty relations for the product and sum of variances of two incompatible observables in a finite dimensional Hilbert space. It is shown that the new uncertainty relations provide near-optimal state-dependent bounds, which can be useful for quantum metrology, entanglement detection etc. in quantum information theory.

It is further shown that the uncertainty relations are related to the "spreads" of the distribution of measurement outcomes caused by incompatible observables. Intuitively, this means that the ability of learning the distribution has both the upper and lower bounds. Combination of these bounds provides naturally an uncertainty interval which captures the essence of uncertainty in quantum theory. Finally, we explain how to employ entropic uncertainty relations to derive lower bounds for the product of variances of incompatible observables.

Received:
Feb 15, 2017
Published:
Feb 20, 2017

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Yunlong Xiao, Nai-Huan Jing, Bing Yu, Shao-Ming Fei and Xianqing Li-Jost

Strong variance-based uncertainty relations and uncertainty intervals