Topological Link Models of Multipartite Entanglement

TL;DR

This paper introduces a topological link-based model for multipartite entanglement, expanding the mathematical framework beyond graphs and hypergraphs, and demonstrates its unique representational capabilities and connections to knot theory.

Contribution

It presents a novel topological link model for entanglement, showing it can represent entropy vectors beyond graph/hypergraph models and extends contraction map proofs to this setting.

Findings

Existence of entropy vectors represented by links not realizable by graphs or hypergraphs

Extension of contraction map proof method to topological links

Connection to complex problems in knot theory

Abstract

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.