Structure of multipartite entanglement in random cluster-like photonic systems

TL;DR

This paper investigates the structure of multipartite entanglement in randomly generated cluster states, revealing that optimal entanglement does not always align with maximum edge density and suggesting small-world structures in quantum networks.

Contribution

It provides a novel analysis of how multipartite entanglement structures emerge in random cluster states across different dimensions, highlighting non-trivial correlations.

Findings

Multipartite entanglement peaks at intermediate edge densities.

Similar entanglement patterns observed in higher-dimensional clusters.

Small-world structures may enhance quantum information sharing.

Abstract

Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how quantum networking, embodied by the generation of a special class of multipartite states called cluster states, can be used to achieve a powerful paradigm for quantum information processing. Here we analyze randomly generated cluster states in order to address the emergence of multipartite correlations as a function of the density of edges in a given underlying graph. We find that the most widespread multipartite entanglement does not correspond to the highest amount of edges in the cluster. We extend the analysis to higher dimensions, finding similar results, which suggest the establishment of small world structures in the entanglement sharing of randomised cluster states, which can be exploited in engineering more efficient quantum information carriers.