SVD entanglement entropy
In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarit...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2024
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| Online Access: | https://hdl.handle.net/1721.1/153284 |
| _version_ | 1811084624911138816 |
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| author | Parzygnat, Arthur J. Takayanagi, Tadashi Taki, Yusuke Wei, Zixia |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Parzygnat, Arthur J. Takayanagi, Tadashi Taki, Yusuke Wei, Zixia |
| author_sort | Parzygnat, Arthur J. |
| collection | MIT |
| description | In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence. |
| first_indexed | 2024-09-23T12:54:31Z |
| format | Article |
| id | mit-1721.1/153284 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:54:31Z |
| publishDate | 2024 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1532842024-07-11T18:54:20Z SVD entanglement entropy Parzygnat, Arthur J. Takayanagi, Tadashi Taki, Yusuke Wei, Zixia Massachusetts Institute of Technology. Department of Mathematics In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence. 2024-01-09T17:24:07Z 2024-01-09T17:24:07Z 2023-12-18 2023-12-31T04:20:38Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/153284 Journal of High Energy Physics. 2023 Dec 18;2023(12):123 PUBLISHER_CC en https://doi.org/10.1007/JHEP12(2023)123 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Parzygnat, Arthur J. Takayanagi, Tadashi Taki, Yusuke Wei, Zixia SVD entanglement entropy |
| title | SVD entanglement entropy |
| title_full | SVD entanglement entropy |
| title_fullStr | SVD entanglement entropy |
| title_full_unstemmed | SVD entanglement entropy |
| title_short | SVD entanglement entropy |
| title_sort | svd entanglement entropy |
| url | https://hdl.handle.net/1721.1/153284 |
| work_keys_str_mv | AT parzygnatarthurj svdentanglemententropy AT takayanagitadashi svdentanglemententropy AT takiyusuke svdentanglemententropy AT weizixia svdentanglemententropy |