Generation of octapartite entanglement by connecting two symmetric cascaded four-wave mixing processes with one linear beam splitter

We theoretically propose a scheme for generating full octapartite entanglement using two symmetric cascaded four-wave mixing (FWM) processes and one linear beam splitter (BS), in which two independent symmetric cascaded FWM processes are connected by a BS. To present the entanglement properties of the system, we first verify that the generated state is a H-graph state by exploiting the graphical calculus for Gaussian pure states, and reveal the internal interaction of the generated state by using the derived coupling strength matrix. We proceed with investigating the possibility of this scheme for generating octapartite entanglement by applying the positivity under a partial transposition criterion. The results show that there exists full octapartite entanglement in the whole gain region, and the degree of entanglement increases as the power gain increases. In addition, we investigate the effect of transmissivity of BS on the entanglement properties of the system and the dependence of bipartite entanglement on the power gain and the transmissivity of BS. Our results give a simple way to increase the scale of entanglement by linear optics and cascaded FWM processes.