Multiboundary Wormholes and Holographic Entanglement

TL;DR

This paper explores the entanglement structure in multiboundary wormholes within the AdS/CFT framework, revealing complex multipartite and bipartite entanglement patterns and developing new analytical tools.

Contribution

It introduces new methods to analyze n-partite entanglement in holographic states and characterizes the entanglement structure across different bulk geometries.

Findings

Entanglement can be entirely multipartite or predominantly bipartite depending on the moduli space region.

Developed new tools for analyzing intrinsic n-partite entanglement.

Established lower bounds on distillable entanglement in multiboundary wormholes.

Abstract

The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS_3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, in some regions of the moduli space the entanglement is almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between at least n-1 parties, and that the distillable entanglement between the asymptotic regions is at least (n+1)/2 partite.