Homological analysis of multi-qubit entanglement

TL;DR

This paper introduces a novel topological approach using persistent homologies to analyze and classify multipartite entanglement in multi-qubit systems, demonstrating effectiveness on small datasets.

Contribution

It presents a new method applying persistent homology to characterize multipartite entanglement using bipartite measures, offering a topological perspective.

Findings

Barcodes effectively classify small multi-qubit entangled states

Persistent homology captures entanglement structures

Method shows promise for entanglement analysis

Abstract

We propose the usage of persistent homologies to characterize multipartite entanglement. On a multi-qubit data set we introduce metric-like measures defined only in terms of bipartite entanglement and then we derive barcodes. We show that they are able to provide a good classification of entangled states, at least for a small number of qubit.