Compact source for quadripartite deterministically entangled optical fields

Since entangled multiple optical fields were identified as the building blocks of quantum networks, the quadripartite entangled optical fields have been produced by using four degenerate optical parametric amplifiers or two nondegenerate optical parametric amplifiers (NOPAs). However, realizing an efficient and compact source for multiple quantum users has remained an outstanding challenge, hindering their practical applications. Here, we proposed a compact and feasible scheme to deterministically entangle four spatially separated optical fields, employing only a single NOPA. Accordingly, two-sided output NOPA-based optical fields were coupled on a beam splitter network to form the quadripartite entangled state, causing the deterministic generation of both the Greenberger–Horne–Zeilinger (GHZ) and the linear cluster states in this compact entanglement source. We also obtained the optimal experimental parameters based on the simulation results, thereby providing a direct reference for experimental implementation. Our findings propose that the resultant GHZ and linear cluster states can be potentially applied in quantum-enhanced information science, specifically in quantum secret sharing, controlled quantum teleportation networks, and quantum-entangled atomic ensemble networks.