Characterizing Entanglement Dimensionality from Randomized Measurements
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an i...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-05-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.4.020324 |
| _version_ | 1797829674874699776 |
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| author | Shuheng Liu Qiongyi He Marcus Huber Otfried Gühne Giuseppe Vitagliano |
| author_facet | Shuheng Liu Qiongyi He Marcus Huber Otfried Gühne Giuseppe Vitagliano |
| author_sort | Shuheng Liu |
| collection | DOAJ |
| description | We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of su(d) bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions d_{a}=d_{b}=d of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario. |
| first_indexed | 2024-04-09T13:25:09Z |
| format | Article |
| id | doaj.art-3d70cda578af4557b0e22dc5d33286f7 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-04-09T13:25:09Z |
| publishDate | 2023-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-3d70cda578af4557b0e22dc5d33286f72023-05-10T14:18:08ZengAmerican Physical SocietyPRX Quantum2691-33992023-05-014202032410.1103/PRXQuantum.4.020324Characterizing Entanglement Dimensionality from Randomized MeasurementsShuheng LiuQiongyi HeMarcus HuberOtfried GühneGiuseppe VitaglianoWe consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of su(d) bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions d_{a}=d_{b}=d of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario.http://doi.org/10.1103/PRXQuantum.4.020324 |
| spellingShingle | Shuheng Liu Qiongyi He Marcus Huber Otfried Gühne Giuseppe Vitagliano Characterizing Entanglement Dimensionality from Randomized Measurements PRX Quantum |
| title | Characterizing Entanglement Dimensionality from Randomized Measurements |
| title_full | Characterizing Entanglement Dimensionality from Randomized Measurements |
| title_fullStr | Characterizing Entanglement Dimensionality from Randomized Measurements |
| title_full_unstemmed | Characterizing Entanglement Dimensionality from Randomized Measurements |
| title_short | Characterizing Entanglement Dimensionality from Randomized Measurements |
| title_sort | characterizing entanglement dimensionality from randomized measurements |
| url | http://doi.org/10.1103/PRXQuantum.4.020324 |
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