Multipartite entanglement via the Mayer-Vietoris theorem

TL;DR

This paper explores the relationship between multipartite entanglement and topology using the Mayer-Vietoris theorem, extending the ER-EPR duality to higher-dimensional tori and encoding entanglement in topological invariants.

Contribution

It generalizes the topological interpretation of entanglement from maximally entangled states to multipartite states using higher-dimensional topological tools.

Findings

Multipartite entanglement can be characterized by higher inclusion maps.

The Mayer-Vietoris sequence encodes multipartite entanglement topologically.

Extension of ER-EPR duality to higher-dimensional tori.

Abstract

The connection between entanglement and topology manifests itself in the form of the ER-EPR duality. This statement however refers to the maximally entangled states only. In this article I study the multipartite entanglement and the way in which it relates to the topological interpretation of the ER-EPR duality. The $2$ dimensional genus $1$ torus will be generalised to a $n$-dimensional general torus, where the information about the multipartite entanglement will be encoded in the higher inclusion maps of the Mayer-Vietorist sequence.