Analysis of urban atmospheric influence on free-space quantum key distribution

Abstract Quantum key distribution (QKD) has been widely deployed in practical applications after decades of development. However, QKD system is easily affected by external environment especially free-space QKD. In this text, we examine two scenarios of free-space QKD in urban environments: satellite to ground and intercity. For satellite to ground QKD, the effects of stray light are analyzed. For intercity link, we discuss the influence of sea salt particles in coastal cities, insoluble and soot particles in inland cities. Our findings indicate that using the telescope with smaller $FOV$ (field of view) and larger aperture diameters in satellite-to-ground QKD can effectively reduce errors induced by stray light. However, the diameter can't be increased infinitely, when exceeding 0.8m, the number of stray photons entering receiver rises rapidly and the QBER (Quantum Bits Error Rate) shows no significant reduction. For intercity QKD, the strength of extinction varies with relative humidity and aerosol particle radius, consequently altering channel transmittance. We investigate the impact of sea salt, insoluble particles, and soot on the key rate, finding that under the number density \(N=10^6/m^3\), sea salt exhibits the strongest impacts on key rate especially when radius exceed 2.5 μm. The impacts of insoluble particles are weaker and soot is the weakest that can be ignored until \(N\) reaches \(10^9/m^3\). For larger particle density, we can get higher key rate and further transmission distances in soot-dominated environment. Our work could provide valuable reference for the practical implementation of QKD in practical urban atmosphere.