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Noise-resolution uncertainty principle in classical and quantum systems

We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A...

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Autores principales: Gureyev, Timur E., Kozlov, Alexander, Paganin, David M., Nesterets, Yakov I., Quiney, Harry M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217923/
https://www.ncbi.nlm.nih.gov/pubmed/32398680
http://dx.doi.org/10.1038/s41598-020-64539-7
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author Gureyev, Timur E.
Kozlov, Alexander
Paganin, David M.
Nesterets, Yakov I.
Quiney, Harry M.
author_facet Gureyev, Timur E.
Kozlov, Alexander
Paganin, David M.
Nesterets, Yakov I.
Quiney, Harry M.
author_sort Gureyev, Timur E.
collection PubMed
description We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the “classical” noise-resolution uncertainty limit. This uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum optics and imaging.
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spelling pubmed-72179232020-05-19 Noise-resolution uncertainty principle in classical and quantum systems Gureyev, Timur E. Kozlov, Alexander Paganin, David M. Nesterets, Yakov I. Quiney, Harry M. Sci Rep Article We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the “classical” noise-resolution uncertainty limit. This uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum optics and imaging. Nature Publishing Group UK 2020-05-12 /pmc/articles/PMC7217923/ /pubmed/32398680 http://dx.doi.org/10.1038/s41598-020-64539-7 Text en © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Gureyev, Timur E.
Kozlov, Alexander
Paganin, David M.
Nesterets, Yakov I.
Quiney, Harry M.
Noise-resolution uncertainty principle in classical and quantum systems
title Noise-resolution uncertainty principle in classical and quantum systems
title_full Noise-resolution uncertainty principle in classical and quantum systems
title_fullStr Noise-resolution uncertainty principle in classical and quantum systems
title_full_unstemmed Noise-resolution uncertainty principle in classical and quantum systems
title_short Noise-resolution uncertainty principle in classical and quantum systems
title_sort noise-resolution uncertainty principle in classical and quantum systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217923/
https://www.ncbi.nlm.nih.gov/pubmed/32398680
http://dx.doi.org/10.1038/s41598-020-64539-7
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