Emergent complex quantum networks in continuous-variables non-Gaussian states

TL;DR

This paper investigates how complex network theory can be applied to analyze the structure and properties of non-Gaussian continuous-variable quantum states, revealing how initial network configurations influence emergent quantum correlations.

Contribution

It introduces a novel approach combining complex network analysis with quantum state characterization, demonstrating the impact of initial network structures on emergent quantum correlations.

Findings

Photon subtraction affects nodes within four steps of the imprinted network.

Emergent network properties like mean and variance increase with photon subtraction.

Structure of the initial network influences higher moments and local behaviors in the emergent network.

Abstract

We use complex network theory to study a class of continuous-variable quantum states that present both multipartite entanglement and non-Gaussian statistics. We consider the intermediate scale of several dozens of components at which such systems are already hard to characterize. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. We then engender non-Gaussian statistics via multiple photon subtraction operations acting on a single node. We replicate in the quantum regime some of the models that mimic real-world complex networks in order to test their structural properties under local operations. We then go beyond the already known single-mode effects, by studying the emergent network of photon-number correlations via complex networks measures. We analytically prove that the imprinted network structure defines a vicinity of nodes, at a distance of four steps from the photon-subtracted node, in which the emergent network changes due to photon subtraction. Moreover, our numerical analysis shows that the emergent structure is greatly influenced by the structure of the imprinted network. Indeed, while the mean and the variance of the degree and clustering distribution of the emergent network always increase, the higher moments of the distributions are governed by the specific structure of the imprinted network. Finally, we show that the behaviour of nearest neighbours of the subtraction node depends on how they are connected to each other in the imprinted structure.