# Multiboundary Wormholes and Holographic Entanglement

**Authors:** Vijay Balasubramanian, Patrick Hayden, Alexander Maloney, Donald Marolf, Simon F. Ross  
**arXiv:** [1406.2663](https://arxiv.org/abs/1406.2663)  
**Date:** 2014-06-10  
**Summary page:** https://www.summarizepaper.com/en/paper/1406.2663v2/

## Key points

- The AdS/CFT correspondence establishes a connection between quantum entanglement in boundary Conformal Field Theories (CFTs) and geometric properties in asymptotically Anti-de Sitter (AdS) space-time.
- Researchers explore different manifestations of dual bulk states in moduli space, ranging from interconnected black holes with wormholes to disconnected components.
- Entanglement is quantified using AdS minimal surfaces, revealing both multipartite and bipartite characteristics based on the region of moduli space.
- Novel analytical tools are introduced to investigate intrinsic n-partite entanglement, showing that certain wormholes exhibit inherent entanglement among at least n-1 parties.
- The study sheds light on complex quantum phenomena within holographic frameworks, enhancing our understanding of multiboundary wormholes and holographic entanglement.

## Summary

The AdS/CFT Correspondence: Unraveling the Connection Between Quantum Entanglement and Geometric Properties

The AdS/CFT correspondence is a fundamental concept in theoretical physics that establishes a profound connection between quantum entanglement in boundary Conformal Field Theories (CFTs) and geometric properties in the dual asymptotically Anti-de Sitter (AdS) space-time. In their research titled "Multiboundary Wormholes and Holographic Entanglement," authors Vijay Balasubramanian, Patrick Hayden, Alexander Maloney, Donald Marolf, and Simon F. Ross delve into this intricate interplay between entangled states within the n-fold tensor product of a 1+1 dimensional CFT Hilbert space and the corresponding Euclidean path integral over a Riemann surface with n holes. Exploring Moduli Space: Different Manifestations of Dual Bulk States

Through their study, the researchers explore various regions of moduli space where the dual bulk state manifests differently. In some instances, it takes on the form of a black hole with n asymptotically AdS_3 regions interconnected by a common wormhole. However, in other scenarios, the bulk disintegrates into disconnected components. By analyzing the entanglement structure within these settings, the team derives explicit wave functions in the puncture limit of the Riemann surface using CFT n-point functions. Utilizing AdS Minimal Surfaces to Quantify Entanglement

In addition to their analysis using CFT methods, Balasubramanian et al. also employ AdS minimal surfaces as a tool to quantify entanglement more broadly. Their findings reveal that entanglement can exhibit both multipartite and bipartite characteristics depending on the specific region of moduli space under consideration. While some configurations display entirely multipartite entanglement patterns that are not of the Greenberger-Horne-Zeilinger (GHZ) type, there are instances where entanglement predominantly occurs between pairs of CFTs, leading to almost exclusively bipartite relationships. Novel Analytical Tools for Investigating Intrinsic n-Partite Entanglement

The team introduces novel analytical tools to investigate intrinsic n-partite entanglement and demonstrates that certain wormholes with similar-sized horizons exhibit inherent entanglement among at least n-1 parties. Moreover, they establish that the distillable entanglement between asymptotic regions is inherently at least (n+1)/2 partite in nature. A Nuanced Exploration: Shedding Light on Complex Quantum Phenomena

This comprehensive analysis presented by Balasubramanian et al. contributes significantly to our understanding of quantum information theory within the context of AdS/CFT duality. By shedding light on complex quantum phenomena within holographic frameworks, their study offers valuable insights into the underlying mechanisms governing multiboundary wormholes and holographic entanglement.