Circular-beam approximation for quantum channels in a turbulent atmosphere

The evolution of quantum states of light in free-space channels is strongly influenced by atmospheric turbulence, posing a significant challenge for quantum communication. The transmittance in such channels randomly fluctuates. This effect is commonly described by the probability distribution of transmittance (PDT). The elliptic-beam approximation provides an analytical model for the PDT, showing good agreement with experimental and simulation data within a specific range of channel parameters. In this work, we introduce the circular-beam approximation -- a simplified alternative that offers satisfactory accuracy while significantly reducing computational complexity. Our method naturally leads to a technique for determining the model parameters from the first two moments of the transmittance. This approach eliminates the model misspecification bias inherent in the elliptic-beam approximation and significantly extends the applicability range of the PDT model, providing a practical tool for characterizing atmospheric channels in quantum applications.