Weighted Uncertainty Relations

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 a...

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Autores principales: Xiao, Yunlong, Jing, Naihuan, Li-Jost, Xianqing, Fei, Shao-Ming
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4794717/
https://www.ncbi.nlm.nih.gov/pubmed/26984295
http://dx.doi.org/10.1038/srep23201
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author Xiao, Yunlong
Jing, Naihuan
Li-Jost, Xianqing
Fei, Shao-Ming
author_facet Xiao, Yunlong
Jing, Naihuan
Li-Jost, Xianqing
Fei, Shao-Ming
author_sort Xiao, Yunlong
collection PubMed
description 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.
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spelling pubmed-47947172016-03-18 Weighted Uncertainty Relations Xiao, Yunlong Jing, Naihuan Li-Jost, Xianqing Fei, Shao-Ming Sci Rep Article 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. Nature Publishing Group 2016-03-17 /pmc/articles/PMC4794717/ /pubmed/26984295 http://dx.doi.org/10.1038/srep23201 Text en Copyright © 2016, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Xiao, Yunlong
Jing, Naihuan
Li-Jost, Xianqing
Fei, Shao-Ming
Weighted Uncertainty Relations
title Weighted Uncertainty Relations
title_full Weighted Uncertainty Relations
title_fullStr Weighted Uncertainty Relations
title_full_unstemmed Weighted Uncertainty Relations
title_short Weighted Uncertainty Relations
title_sort weighted uncertainty relations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4794717/
https://www.ncbi.nlm.nih.gov/pubmed/26984295
http://dx.doi.org/10.1038/srep23201
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AT jingnaihuan weighteduncertaintyrelations
AT lijostxianqing weighteduncertaintyrelations
AT feishaoming weighteduncertaintyrelations

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