Theory of atmospheric quantum channels based on the law of total probability

TL;DR

This paper develops a theoretical framework for atmospheric quantum channels using the law of total probability, deriving probability distributions for transmittance affected by turbulence, and analyzing implications for quantum communication security.

Contribution

It introduces a novel method to derive the probability distribution of transmittance in atmospheric channels considering turbulence effects, unifying beam wandering and distortions.

Findings

Derived PDT varies from log-negative Weibull to truncated log-normal distributions.

The method enables consistent description of beam tracking in quantum communication.

Beam tracking does not always enhance quantum key exchange security.

Abstract

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. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improves quantum communication.