Beyond the Holographic Entropy Cone via Cycle Flows
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220_2024_5120_ReferencePDF.pdf
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Author(s)
He, Temple
Hernández-Cuenca, Sergio
Keeler, Cynthia
Date Issued
October 12, 2024
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
He, T., Hernández-Cuenca, S. & Keeler, C. Beyond the Holographic Entropy Cone via Cycle Flows. Commun. Math. Phys. 405, 252 (2024).
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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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.
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DOI of Published Version
https://doi.org/10.1007/s00220-024-05120-5
