Generating Honeycomb-Structured Entanglement with a Reconfigurable Spatially Structured Pump.

Multipartite entanglement is a fundamental resource for quantum information processing. Various degrees of freedom of light, such as time, frequency, and space, have been widely exploited to create large-scale entangled quantum sources, enhancing information transmission capacity. Here, we demonstrate the generation of honeycomb-structured entanglement among 13 spatially separated beams with a reconfigurable pump field of a hexagonal structure, featuring the simultaneous multiplexing of 18 four-wave mixing processes within a single atomic ensemble. Such a reconfigurable spatially structured pump is constructed by loading a reprogrammable hologram onto a spatial light modulator. Additionally, we analyze 8190 possible steering bipartitions and examine the robustness of the quantum properties inherent in the system. Furthermore, by reconfiguring the pump fields with square, hexagonal, and eightfold quasicrystal structures, we can generate square-, hexagonal-, and octagonal-structured output fields. This enables the output mode number to be extended from 9 and 19 up to 21. These results provide a promising route to realizing spatially programmable multipartite entanglement, enabling reconfigurable multiuser quantum communication networks, and suggesting potential avenues toward exploring topological phenomena in continuous-variable quantum systems.