Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere

Our study investigates the presence of high-dimensional entanglement in a recent demonstration of a noise-resistant quantum key distribution (QKD) protocol presented in [Phys. Rev. X 13, 021001 (2023)]. We determined that it is possible to certify the dimensionality of the distributed entangled states to be at least three. To demonstrate this, we developed an energy-time entanglement discretization technique, as well as an improved witness for entanglement dimensionality. Our results provide insight into the complex relationship between high-dimensional entanglement and the noise resistance of QKD protocols operating in high dimensions.