Stochastic Modeling of a Memory-Assisted Measurement-Device-Independent Quantum Key Distribution System in Free-Space Metropolitan Environments

On the pathway to quantum key distribution on a global scale, will be the realization of metropolitan-sized Memory Assisted Measurement-Device-Independent Quantum Key Distribution (MA-MDI-QKD) systems. Here, we present a simplistic and intuitive stochastic model to predict key distribution rates in a MA-MDI-QKD scheme that addresses the real-world parameters inherent to free-space quantum communication channels. Specific to our algorithm, the memory-assisted based system allows us to leverage the advantage of asynchronously loaded quantum memory when predicting the distribution rates. Specifically, by focusing on metropolitan distances, we perform simulations tailored toward a system based on free-space links and field-deployable quantum memory. We show the capabilities of our model to predict key rate distributions over ranges of 10-50 km for a set of atmospheric-based parameters and selection of QM efficiencies and coherence times. This tool provides impactful insights into the deployment and optimization of practical MA-MDI-QKD networks in urban environments. Our streamlined approach is a valuable addition to existing quantum network simulators for the smooth integration of quantum networking into the field of communications engineering.