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Quantum Entropy Information Measures Quantum Optimization

Combinatorial properties of holographic entropy inequalities

arXiv
Authors: Guglielmo Grimaldi, Matthew Headrick, Veronika E. Hubeny, Pavel Shteyner

Year

2026

Paper ID

3802

Status

Preprint

Abstract Read

~2 min

Abstract Words

113

Citations

N/A

Abstract

A holographic entropy inequality (HEI) is a linear inequality obeyed by Ryu-Takayanagi holographic entanglement entropies, or equivalently by the minimum cut function on weighted graphs. We establish a new combinatorial framework for studying HEIs, and use it to prove several properties they share, including two majorization-related properties as well as a necessary and sufficient condition for an inequality to be an HEI. We thereby resolve all the conjectures presented in [arXiv:2508.21823], proving two of them and disproving the other two. In particular, we show that the null reduction of any superbalanced HEI passes the majorization test defined in [arXiv:2508.21823], thereby providing strong new evidence that all HEIs are obeyed in time-dependent holographic states.

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  • This paper contributes to the Quantum Optimization research area in the Quantum Articles archive.
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  • A holographic entropy inequality (HEI) is a linear inequality obeyed by Ryu-Takayanagi holographic entanglement entropies, or equivalently by the minimum cut function on...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.09987 [2] arXiv https://arxiv.org/abs/2601.09987 [3] Publisher https://arxiv.org/abs/2601.09987

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