Entanglement Distribution in the Quantum Internet: An Optimal Decision Problem Formulation

The entanglement distribution process is widely en-visioned as one of the key functionalities of the Quantum Internet. Its engineering is, thus, foundational to effectively implement communication protocols in quantum networks. In this paper, we exploit the Markov Decision Process formalism to model the entanglement distribution as an optimal decision problem. Furthermore, we analyze the impact of reward functions on two key performance metrics, namely: the average distribution time and the average distributed cluster size. From this analysis, we gain some insights for choosing a reward function that meets suitable figures of merit for an overlaying communication protocol.