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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...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2020
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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. |
format | Online Article Text |
id | pubmed-7217923 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
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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