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arXiv · 2606.00210

Constraints on four-party entanglement in holography

Vijay Balasubramanian·William K. L. Chan·Monica Jinwoo Kang·Chitraang Murdia·Simon F. Ross
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Abstract

We show that in pure time-reflection-symmetric holographic states several known four-party entanglement signals vanish unless the triple information $I_3$ is non-zero. In this sense, our results show that $I_3$ is the strongest known signal of the presence of quadripartite entanglement. Additionally, $I_3$ quantitatively bounds all four-party entanglement signals built from the multi-entropy. However, the residual entropy $Q_4$, also a measure of four-party entanglement, is not bounded by $I_3$, although $I_3=0$ does imply $Q_4=0$ for holographic states (except on a set of measure zero for which $Q_4$ is ill-defined).

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Vijay Balasubramanian, William K. L. Chan, Monica Jinwoo Kang, Chitraang Murdia, Simon F. Ross. 2026-05-29. Constraints on four-party entanglement in holography. https://arxiv.org/abs/2606.00210

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