An algorithm to explore entanglement in small systems
A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize o...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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The Royal Society Publishing
2018
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6030646/ https://www.ncbi.nlm.nih.gov/pubmed/29977130 http://dx.doi.org/10.1098/rspa.2018.0023 |
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author | Reuvers, R. |
author_facet | Reuvers, R. |
author_sort | Reuvers, R. |
collection | PubMed |
description | A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels. |
format | Online Article Text |
id | pubmed-6030646 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-60306462018-07-05 An algorithm to explore entanglement in small systems Reuvers, R. Proc Math Phys Eng Sci Research Articles A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels. The Royal Society Publishing 2018-06 2018-06-13 /pmc/articles/PMC6030646/ /pubmed/29977130 http://dx.doi.org/10.1098/rspa.2018.0023 Text en © 2018 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Articles Reuvers, R. An algorithm to explore entanglement in small systems |
title | An algorithm to explore entanglement in small systems |
title_full | An algorithm to explore entanglement in small systems |
title_fullStr | An algorithm to explore entanglement in small systems |
title_full_unstemmed | An algorithm to explore entanglement in small systems |
title_short | An algorithm to explore entanglement in small systems |
title_sort | algorithm to explore entanglement in small systems |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6030646/ https://www.ncbi.nlm.nih.gov/pubmed/29977130 http://dx.doi.org/10.1098/rspa.2018.0023 |
work_keys_str_mv | AT reuversr analgorithmtoexploreentanglementinsmallsystems AT reuversr algorithmtoexploreentanglementinsmallsystems |