Beyond the Holographic Entropy Cone via Cycle Flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910671716745216 |
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| author | He, Temple Hernández-Cuenca, Sergio Keeler, Cynthia |
| author_facet | He, Temple Hernández-Cuenca, Sergio Keeler, Cynthia |
| contents | Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10137 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Beyond the Holographic Entropy Cone via Cycle Flows He, Temple Hernández-Cuenca, Sergio Keeler, Cynthia High Energy Physics - Theory Combinatorics Quantum Physics Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs. |
| title | Beyond the Holographic Entropy Cone via Cycle Flows |
| topic | High Energy Physics - Theory Combinatorics Quantum Physics |
| url | https://arxiv.org/abs/2312.10137 |