Multipartite Reflected Entropy

TL;DR

This paper introduces two methods to construct bulk geometries in AdS/CFT with minimal surfaces related to multipartite reflected entropy, providing new insights into entanglement structures in holography.

Contribution

It proposes novel geometric constructions for multipartite reflected entropy using cyclic gluing and canonical purification, extending the understanding of entanglement in holographic theories.

Findings

Minimal surfaces correspond to candidate multipartite reflected entropies.

Construction relates boundary states to multiboundary wormholes in AdS3/CFT2.

Conjecture extends the boundary interpretation to higher dimensions.

Abstract

We discuss two methods that, through a combination of cyclically gluing copies of a given $n$-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the $n$-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the $n$-party reflected entropy. In the context of AdS$_3$/CFT$_2$, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions.