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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

Published May 29, 2026• 0 citations
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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).

DOI
10.48550/arxiv.2606.00210

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A bstract We study multiparty entanglement signals, which are functions of a quantum state that are non-zero only when the state has multiparty entanglement. We consider known signals of three- and four-party entanglement, and propose new signals for four- and higher-party entanglement. We make some remarks on their general properties, but mainly focus on using holographic states in AdS 3 /CFT 2 as a test case to explore their properties. For both the AdS vacuum and multiboundary wormhole states, we find that the multiparty entanglement signals are generically non-zero and of order one in units of the central charge of the dual CFT, revealing substantial multiparty entanglement. In the large-horizon limit of multiboundary wormhole states, however, the signals for three or more parties become small, indicating the short-range nature of entanglement.
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