Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
Abstract We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension $$d \ge 3$$ d ≥ 3 , a form of entanglement exists that is hard to detect and called bound entangle...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-02-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-29211-w |
| _version_ | 1811171781130584064 |
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| author | Christopher Popp Beatrix C. Hiesmayr |
| author_facet | Christopher Popp Beatrix C. Hiesmayr |
| author_sort | Christopher Popp |
| collection | DOAJ |
| description | Abstract We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension $$d \ge 3$$ d ≥ 3 , a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Extending analytical and numerical methods and results for Bell diagonal qutrits ( $$d=3$$ d = 3 ), we successfully classify more than $$75\%$$ 75 % of representative Bell diagonal PPT states for $$d=4$$ d = 4 . Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts ( $$d=4$$ d = 4 ). We find that at least $$75.7\%$$ 75.7 % of all PPT states are separable, $$1.7\%$$ 1.7 % bound entangled and for $$22.6\%$$ 22.6 % it remains unclear whether they are separable or bound entangled. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits ( $$d=3$$ d = 3 ) and ququarts ( $$d=4$$ d = 4 ). Finally, using a detailed visual analysis of the set of separable and bound entangled Bell diagonal states in both dimensions, qualitative observations are made that allow to better distinguish bound entangled from separable states. |
| first_indexed | 2024-04-10T17:19:46Z |
| format | Article |
| id | doaj.art-b9f9d90dab644bec859de0532865512c |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-10T17:19:46Z |
| publishDate | 2023-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-b9f9d90dab644bec859de0532865512c2023-02-05T12:09:53ZengNature PortfolioScientific Reports2045-23222023-02-0113111510.1038/s41598-023-29211-wComparing bound entanglement of bell diagonal pairs of qutrits and ququartsChristopher Popp0Beatrix C. Hiesmayr1Faculty of Physics, University of ViennaFaculty of Physics, University of ViennaAbstract We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension $$d \ge 3$$ d ≥ 3 , a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Extending analytical and numerical methods and results for Bell diagonal qutrits ( $$d=3$$ d = 3 ), we successfully classify more than $$75\%$$ 75 % of representative Bell diagonal PPT states for $$d=4$$ d = 4 . Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts ( $$d=4$$ d = 4 ). We find that at least $$75.7\%$$ 75.7 % of all PPT states are separable, $$1.7\%$$ 1.7 % bound entangled and for $$22.6\%$$ 22.6 % it remains unclear whether they are separable or bound entangled. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits ( $$d=3$$ d = 3 ) and ququarts ( $$d=4$$ d = 4 ). Finally, using a detailed visual analysis of the set of separable and bound entangled Bell diagonal states in both dimensions, qualitative observations are made that allow to better distinguish bound entangled from separable states.https://doi.org/10.1038/s41598-023-29211-w |
| spellingShingle | Christopher Popp Beatrix C. Hiesmayr Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts Scientific Reports |
| title | Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| title_full | Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| title_fullStr | Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| title_full_unstemmed | Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| title_short | Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| title_sort | comparing bound entanglement of bell diagonal pairs of qutrits and ququarts |
| url | https://doi.org/10.1038/s41598-023-29211-w |
| work_keys_str_mv | AT christopherpopp comparingboundentanglementofbelldiagonalpairsofqutritsandququarts AT beatrixchiesmayr comparingboundentanglementofbelldiagonalpairsofqutritsandququarts |