For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$
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abstract
We study multipartite entanglement in typical pure states holographically dual to pure BTZ black holes, using multi-entropy and its ``genuine'' version. In the bulk, these quantities are computed by minimal geodesic networks (so-called Steiner trees). We find that at sufficiently high temperature, the genuine tripartite multi-entropy exhibits a volume-law scaling in sharp contrast to vacuum AdS$_3$, where the genuine contribution is universal and size-independent. Moreover, we find another phase: once one subsystem exceeds half of the total system, the leading genuine tripartite entanglement vanishes and reduces to that for global AdS${}_3$. This transition is indeed consistent with recent arguments for distillable EPR pairs in tripartite Haar-random states. Motivated by finite-cutoff holography, we further study the radial cutoff dependence of multi-entropy and show that genuine multi-entropy acquires nontrivial size dependence even for the tripartite case in AdS${}_3$. As a byproduct, we also observe an intriguing ``area-law'' contribution to multi-entropy that is relevant to vacuum AdS${}_3$.
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The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.
citing papers explorer
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Multi-entropy in random tensor networks
For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
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The Entanglement Wedge Polygon
The entanglement wedge polygon volume is proposed as a holographic probe of multipartite entanglement; in AdS3 it is topologically quantized, and a mixed-state generalization is constructed.
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Multi-entropy in heavy local quenches
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
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The Junction Law for Multipartite Entanglement in Confining Holographic Backgrounds
The junction law for multipartite entanglement persists in confining holographic backgrounds, but phase structure and GM short-distance scaling (L^{-4}, L^{-2}, or L^{-2}(log L)^2) are background-dependent.