Entangled states from simple quantum graphs

Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to generate entangled states through coherent control operations between two simple quantum graphs. A controlled operation is defined such that the scattering behavior of one quantum graph dynamically modifies the other. Our analysis reveals the precise conditions under which maximal entanglement or separability arises, including configurations that can be implemented via phase shifts in graph structures. Our findings demonstrate that the maximal entanglement in this system is closely related to recent results on randomized quantum graphs. These results provide new pathways for engineering entanglement using simple quantum graphs and suggest experimental feasibility using microwave networks.