Gigh-dimensional temporal mode propagation in a turbulent environment

Temporal modes of photonic quantum states, intrinsically possess high dimensional Hilbert spaces, provide a new framework to develop a robust free-space quantum key distribution (QKD) scheme in a maritime environment. We show that the high-dimensional temporal modes can be used to fulfill a persistent communication channel to achieve high photon-efficiency even in severe weather conditions. We identify the parameter regimes that allow for a high-fidelity quantum information transmission. We also examine how the turbulent environment affects fidelity and entanglement degree in various environ-mental settings.