Free versus bound entanglement, a NP-hard problem tackled by machine learning

Abstract Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entangleme...

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Autor principal:	Beatrix C. Hiesmayr
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/636ea1ea90104a98a623300f4d0a620a
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spelling	oai:doaj.org-article:636ea1ea90104a98a623300f4d0a620a2021-12-02T18:37:08ZFree versus bound entanglement, a NP-hard problem tackled by machine learning10.1038/s41598-021-98523-62045-2322https://doaj.org/article/636ea1ea90104a98a623300f4d0a620a2021-10-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-98523-6https://doaj.org/toc/2045-2322Abstract Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find $$82\%$$ 82 % to be free entangled, $$2\%$$ 2 % to be certainly separable and as much as $$10\%$$ 10 % to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining $$6\%$$ 6 % of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.Beatrix C. HiesmayrNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Beatrix C. Hiesmayr Free versus bound entanglement, a NP-hard problem tackled by machine learning
description	Abstract Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find $$82\%$$ 82 % to be free entangled, $$2\%$$ 2 % to be certainly separable and as much as $$10\%$$ 10 % to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining $$6\%$$ 6 % of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.
format	article
author	Beatrix C. Hiesmayr
author_facet	Beatrix C. Hiesmayr
author_sort	Beatrix C. Hiesmayr
title	Free versus bound entanglement, a NP-hard problem tackled by machine learning
title_short	Free versus bound entanglement, a NP-hard problem tackled by machine learning
title_full	Free versus bound entanglement, a NP-hard problem tackled by machine learning
title_fullStr	Free versus bound entanglement, a NP-hard problem tackled by machine learning
title_full_unstemmed	Free versus bound entanglement, a NP-hard problem tackled by machine learning
title_sort	free versus bound entanglement, a np-hard problem tackled by machine learning
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/636ea1ea90104a98a623300f4d0a620a
work_keys_str_mv	AT beatrixchiesmayr freeversusboundentanglementanphardproblemtackledbymachinelearning
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Free versus bound entanglement, a NP-hard problem tackled by machine learning

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