Generation of Scalable Genuine Multipartite Gaussian Entanglement with a Parametric Amplifier Network

Genuine multipartite entanglement is a valuable resource in quantum information science, as it exhibits stronger non-locality compared to bipartite entanglement. This non-locality can be exploited in various quantum information protocols, such as teleportation, dense coding, and quantum interferometry. Here, we propose a scheme to generate scalable genuine multipartite continuous-variable entangled states of light using a parametric amplifier network. We verify the presence of genuine quadripartite, hexapartite, and octapartite entanglement through a violation of the positive partial transpose (PPT) criteria. Additionally, we use $\alpha$-entanglement of formation to demonstrate the scalability of our approach to an arbitrary number of $2N$ genuinely entangled parties by taking advantage of the symmetries present in our scheme.