Tripartite Form Universality in Holographic Entropy Inequalities
Abstract
To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.
Related
- Holographic entropy inequalities & typical states
- Relative entropy of entanglement and tripartite minimal surface
- Gravitational form factors of the proton in the improved holographic QCD model
- Gravitational form factors of the pion in light-front holographic QCD
- Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk
BibTeX
@misc{hubeny2026tripartite,
title = {{Tripartite Form Universality in Holographic Entropy Inequalities}},
author = {Veronika E. Hubeny and Yu Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.22504},
eprint = {2609.22504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tripartite Form Universality in Holographic Entropy Inequalities
AU - Veronika E. Hubeny
AU - Yu Liu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.22504
UR - https://arxiv.org/abs/2609.22504
AB - To elucidate the meaning of holographic entropy inequalities (beyond subadditivity) which characterize the entanglement structure of geometric states in holography, arXiv:2309.06296 proposed the "tripartite form" for these inequalities, consisting of tripartite information and conditional tripartite information terms with unit coefficients. While this provides a compact and useful packaging of the inequalities, it is not a priori guaranteed that all inequalities can be recast in this form. Here we conjecture that they can, and present substantial evidence, by proving that the two known infinite families of holographic entropy inequalities found in arXiv:2309.15145 can indeed be written in the tripartite form. This is significant because such recasting is particularly nontrivial for these families. Apart from providing the explicit tripartite form expressions for every member of these two infinite families, we detail how we arrived at them, in the process deriving several useful identities which may serve as stepping stones to formulate further repackaging of the corresponding information quantities. We also illustrate the power of the tripartite form by proving a number of structural properties satisfied by any holographic entropy inequality.
ER -