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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...

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Autores principales: Nape, Isaac, Rodríguez-Fajardo, Valeria, Zhu, Feng, Huang, Hsiao-Chih, Leach, Jonathan, Forbes, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2021
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.
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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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