Reflected entropy in random tensor networks. Part III. Triway cuts
Abstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these sta...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2024)209 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841559929364676608 |
|---|---|
| author | Chris Akers Thomas Faulkner Simon Lin Pratik Rath |
| author_facet | Chris Akers Thomas Faulkner Simon Lin Pratik Rath |
| author_sort | Chris Akers |
| collection | DOAJ |
| description | Abstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut. |
| format | Article |
| id | doaj-art-f5e0cba9c9ec4c0bbe6047fb0f94f6e8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-f5e0cba9c9ec4c0bbe6047fb0f94f6e82025-01-05T12:06:25ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241217010.1007/JHEP12(2024)209Reflected entropy in random tensor networks. Part III. Triway cutsChris Akers0Thomas Faulkner1Simon Lin2Pratik Rath3Department of Physics and Center for Theory of Quantum Matter, University of Colorado BoulderDepartment of Physics, University of IllinoisNew York University Abu DhabiCenter for Theoretical Physics and Department of Physics, University of California, BerkeleyAbstract For general random tensor network states at large bond dimension, we prove that the integer Rényi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer Rényi parameters, suggested by the triway cut problem, implies the holographic conjecture S R = 2EW, where S R is the reflected entropy and EW is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.https://doi.org/10.1007/JHEP12(2024)209AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Chris Akers Thomas Faulkner Simon Lin Pratik Rath Reflected entropy in random tensor networks. Part III. Triway cuts Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Reflected entropy in random tensor networks. Part III. Triway cuts |
| title_full | Reflected entropy in random tensor networks. Part III. Triway cuts |
| title_fullStr | Reflected entropy in random tensor networks. Part III. Triway cuts |
| title_full_unstemmed | Reflected entropy in random tensor networks. Part III. Triway cuts |
| title_short | Reflected entropy in random tensor networks. Part III. Triway cuts |
| title_sort | reflected entropy in random tensor networks part iii triway cuts |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP12(2024)209 |
| work_keys_str_mv | AT chrisakers reflectedentropyinrandomtensornetworkspartiiitriwaycuts AT thomasfaulkner reflectedentropyinrandomtensornetworkspartiiitriwaycuts AT simonlin reflectedentropyinrandomtensornetworkspartiiitriwaycuts AT pratikrath reflectedentropyinrandomtensornetworkspartiiitriwaycuts |