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Measuring dimensionality and purity of high-dimensional entangled states
High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open chal...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8397747/ https://www.ncbi.nlm.nih.gov/pubmed/34453058 http://dx.doi.org/10.1038/s41467-021-25447-0 |
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author | Nape, Isaac Rodríguez-Fajardo, Valeria Zhu, Feng Huang, Hsiao-Chih Leach, Jonathan Forbes, Andrew |
author_facet | Nape, Isaac Rodríguez-Fajardo, Valeria Zhu, Feng Huang, Hsiao-Chih Leach, Jonathan Forbes, Andrew |
author_sort | Nape, Isaac |
collection | PubMed |
description | High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach. |
format | Online Article Text |
id | pubmed-8397747 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-83977472021-09-22 Measuring dimensionality and purity of high-dimensional entangled states Nape, Isaac Rodríguez-Fajardo, Valeria Zhu, Feng Huang, Hsiao-Chih Leach, Jonathan Forbes, Andrew Nat Commun Article High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach. Nature Publishing Group UK 2021-08-27 /pmc/articles/PMC8397747/ /pubmed/34453058 http://dx.doi.org/10.1038/s41467-021-25447-0 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/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/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Nape, Isaac Rodríguez-Fajardo, Valeria Zhu, Feng Huang, Hsiao-Chih Leach, Jonathan Forbes, Andrew Measuring dimensionality and purity of high-dimensional entangled states |
title | Measuring dimensionality and purity of high-dimensional entangled states |
title_full | Measuring dimensionality and purity of high-dimensional entangled states |
title_fullStr | Measuring dimensionality and purity of high-dimensional entangled states |
title_full_unstemmed | Measuring dimensionality and purity of high-dimensional entangled states |
title_short | Measuring dimensionality and purity of high-dimensional entangled states |
title_sort | measuring dimensionality and purity of high-dimensional entangled states |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8397747/ https://www.ncbi.nlm.nih.gov/pubmed/34453058 http://dx.doi.org/10.1038/s41467-021-25447-0 |
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