Bit Threads and Holographic Monogamy
Abstract Bit threads provide an alternative description of holographic entanglement, replacing the Ryu–Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information property of holographic entanglement entropies. This...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/131553 |
| _version_ | 1811074410175528960 |
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| author | Cui, Shawn X Hayden, Patrick He, Temple Headrick, Matthew Stoica, Bogdan Walter, Michael |
| author_facet | Cui, Shawn X Hayden, Patrick He, Temple Headrick, Matthew Stoica, Bogdan Walter, Michael |
| author_sort | Cui, Shawn X |
| collection | MIT |
| description | Abstract
Bit threads provide an alternative description of holographic entanglement, replacing the Ryu–Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information property of holographic entanglement entropies. This is accomplished using the concept of a so-called multicommodity flow, adapted from the network setting, and tools from the theory of convex optimization. Based on the bit thread picture, we conjecture a general ansatz for a holographic state, involving only bipartite and perfect-tensor type entanglement, for any decomposition of the boundary into four regions. We also give new proofs of analogous theorems on networks. |
| first_indexed | 2024-09-23T09:49:01Z |
| format | Article |
| id | mit-1721.1/131553 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:49:01Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1315532021-09-21T03:55:30Z Bit Threads and Holographic Monogamy Cui, Shawn X Hayden, Patrick He, Temple Headrick, Matthew Stoica, Bogdan Walter, Michael Abstract Bit threads provide an alternative description of holographic entanglement, replacing the Ryu–Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information property of holographic entanglement entropies. This is accomplished using the concept of a so-called multicommodity flow, adapted from the network setting, and tools from the theory of convex optimization. Based on the bit thread picture, we conjecture a general ansatz for a holographic state, involving only bipartite and perfect-tensor type entanglement, for any decomposition of the boundary into four regions. We also give new proofs of analogous theorems on networks. 2021-09-20T17:20:21Z 2021-09-20T17:20:21Z 2019-07-06 2020-09-24T20:51:29Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131553 en https://doi.org/10.1007/s00220-019-03510-8 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Cui, Shawn X Hayden, Patrick He, Temple Headrick, Matthew Stoica, Bogdan Walter, Michael Bit Threads and Holographic Monogamy |
| title | Bit Threads and Holographic Monogamy |
| title_full | Bit Threads and Holographic Monogamy |
| title_fullStr | Bit Threads and Holographic Monogamy |
| title_full_unstemmed | Bit Threads and Holographic Monogamy |
| title_short | Bit Threads and Holographic Monogamy |
| title_sort | bit threads and holographic monogamy |
| url | https://hdl.handle.net/1721.1/131553 |
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