Einstein–Podolsky–Rosen steering based on hexapartite coherent feedback control in four-wave mixing with a spatially structured pump

Quantum steering, as a fundamental resource in quantum information science, is a key resource for secure quantum communication networks. Coherent feedback control (CFC) has been widely used to enhance squeezing. In this paper, we utilize a variable beam splitter (VBS) with a reflectivity of k as the feedback controller to build a coherent feedback control system in four-wave mixing (FWM) processes with a spatially structured pump (SSP). We investigate the influence of feedback strength and interaction intensity on quantum steering across different modes under specific phase delay conditions. The results show that the coherent feedback control system can flexibly control quantum steering. By adjusting the parameters, we can achieve various quantum steering types, especially collective multipartite steering and genuine multipartite steering. It has significant practical application value for secure quantum information processing and offers a theoretical reference for the construction of large-scale, secure quantum networks.