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arXiv:2507.12947 · Physical Review A

Circular-beam approximation for quantum channels in a turbulent atmosphere

I. Pechonkin, M. Klen, A. A. Semenov

Published Nov 25, 2025• 0 citations
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Abstract

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.

DOI
10.1103/pv7j-4zpf

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•Mar 31, 2018•0 citations
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.
Atmospheric turbulence is one of the lead disturbance factors for free-space quantum communication. The quantum states of light in such channels are affected by fluctuating losses characterized by the probability distribution of transmittance (PDT). We obtain the PDT for different horizontal links via numerical simulations of light transmission through the atmosphere. The results are compared with analytical models: the truncated log-normal distribution, the beam-wandering model, the elliptic-beam approximation, and the model based on the law of total probability. Their applicability is shown to be strongly dependent on the receiver aperture radius. We introduce an empirical model based on the Beta distribution, which is in good agreement with numerical simulations for a wide range of channel parameters. However, there are still scenarios where none of the above analytical models fits the numerically simulated data. The numerical simulation is then used to analyze the transmission of quadrature-squeezed light through free-space channels.
Many fundamental and applied experiments in quantum optics require transferring nonclassical states of light through large distances. In this context the free-space channels are a very promising alternative to optical fibers as they are mobile and enable to establish communications with moving objects, using satellites for global quantum links. For such channels the atmospheric turbulence is the main disturbing factor. The statistical properties of the fluctuating transmittance through the turbulent atmosphere are given by the probability distribution of transmittance (PDT). We derive the consistent PDTs for the atmospheric quantum channels by step-by-step inclusion of various atmospheric effects such as beam wandering, beam broadening and deformation of the beam into elliptic form, beam deformations into arbitrary forms. We discuss the applicability of PDT models for different propagation distances and optical turbulence strengths in the case when the receiver module has an annular aperture. We analyze the optimal detection and correction strategies which can improve the channel transmission characteristics. The obtained results are important for the design of optical experiments including postselection and adaptive strategies and for the security analysis of quantum communication protocols in freespace.
Quantum light propagation through turbulent atmosphere has become a subject of intensive research, spanning both theoretical and experimental studies. This interest is driven by its important applications in free-space quantum communication, remote quantum sensing, and environmental monitoring. At the same time, this phenomenon itself poses an intriguing fundamental problem. A consistent theoretical description typically makes explicit assumptions about the measurement scheme at the receiver station and/or the method of quantum-information encoding. A common and straightforward approach encodes the information in quantum states of a quasi-monochromatic mode, representing a pulsed Gaussian beam. Atmospheric turbulence induces random distortions of the pulse shape and, consequently, random fluctuations of the transmittance through the receiver aperture. These fluctuations, characterized by the probability distribution of transmittance (PDT), directly affect the quantum state of the received light. In this paper we examine various analytical models of the PDT, validate them through numerical simulations, and assess their range of applicability. Furthermore, we extend the analysis beyond the standard ensemble-averaging approach, recognizing that realistic experiments typically involve time averaging. This requires a detailed examination of the underlying random process, including the study of temporal correlations and their impact on nonclassical properties of electromagnetic radiation.
The free-space transfer of high-fidelity optical signals between remote locations has many applications, including both classical and quantum communication, precision navigation, clock synchronization, etc. The physical processes that contribute to signal fading and loss need to be carefully analyzed in the theory of light propagation through the atmospheric turbulence. Here we derive the probability distribution for the atmospheric transmittance including beam wandering, beam shape deformation, and beam-broadening effects. Our model, referred to as the elliptic beam approximation, applies to weak, weak-to-moderate, and strong turbulence and hence to the most important regimes in atmospheric communication scenarios.
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristic of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improve quantum communication.
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristics of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking---a procedure which is typically used in practical long-distance free-space quantum communication. Eventually, we analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking not always improves quantum communication.