Multipartite entanglement and topology in holography

TL;DR

This paper explores how multipartite entanglement in holography relates to the topology of the spacetime, using a purification process that involves gluing multiple copies and analyzing minimal surfaces and flows.

Contribution

It introduces a novel purification procedure for multipartite entanglement wedges and links their geometric features to topological properties in holography.

Findings

Multipartite entanglement wedge cross sections map to non-trivial minimal surfaces.

Bipartite cross sections correspond to minimal wormhole throats.

Maximal flows can be glued to form multiflows, revealing topological connections.

Abstract

Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.