Generation of twelve-partite entanglement from two symmetric four-wave mixing processes

Entanglement shared by multipartite is an important resource for quantum technologies. Recently, the hexapartite entanglement generated from the four-wave mixing (FWM) process with a spatially structured pump (SSP) has been experimentally demonstrated (Zhang et al., 2020). To further increase the number of entangled beams, we theoretically propose a scheme for generating twelve-partite entanglement based on two independent symmetric FWM processes with a SSP and one linear beam splitter (BS). The entanglement properties are analyzed by utilizing the positivity under partial transposition criterion, and we find that there is twelve-partite entanglement in the whole interaction region and the degree of entanglement increases as the interaction time increases. In addition, we investigate the dependence of entanglement characteristics of the system on transmissivity of BS and eigenmode structure embedded within the system as well to further study the underlying entanglement structure. Our results pave the way for the experimental generation of multipartite entanglement from the SSP-based FWM process.