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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
22/2019

A Note on the Strong Unitary Uncertainty Relations

Xiaofen Huang, Ting-Gui Zhang, Xianqing Li-Jost, Yuan-Hong Tao and Shao-Ming Fei

Abstract

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)].

Received:
Feb 11, 2019
Published:
Feb 14, 2019

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inJournal
2019 Journal Open Access
Xiaofen Huang, Ting-Gui Zhang, Xianqing Li-Jost, Yuan-Hong Tao and Shao-Ming Fei

A note on the strong unitary uncertainty relations

In: Journal of applied and theoretical physics research, 3 (2019) 1, pp. 1-3