On the Transmission Probabilities in Quantum Key Distribution Systems over FSO Links

TL;DR

This paper analyzes transmission probabilities in quantum key distribution over free-space optical links, considering realistic pointing errors and various fading channels, providing approximate and asymptotic expressions for system performance.

Contribution

It introduces a generalized model for transmission probabilities in QKD over FSO links with stochastic pointing errors and derives new approximate and asymptotic formulas.

Findings

Derived approximate expressions for transmission probabilities.

Presented asymptotic analysis revealing diversity order and array gain.

Connected outage probability over Beckmann fading channels to system parameters.

Abstract

In this paper, we investigate the transmission probabilities in three cases (depending only on the legitimate receiver, depending only the eavesdropper, and depending on both legitimate receiver and eavesdropper) in quantum key distribution (QKD) systems over free-space optical links. To be more realistic, we consider a generalized pointing error scenario, where the azimuth and elevation pointing error angles caused by stochastic jitters and vibrations in the legitimate receiver platform are independently distributed according to a non-identical normal distribution. Taking these assumptions into account, we derive approximate expressions of transmission probabilities by using the Gaussian quadrature method. To simplify the expressions and get some physical insights, some asymptotic analysis on the transmission probabilities is presented based on asymptotic expression for the generalized Marcum Q-function when the telescope gain at the legitimate receiver approaches to infinity. Moreover, from the asymptotic expression for the generalized Marcum Q-function, the asymptotic outage probability over Beckmann fading channels (a general channel model including Rayleigh, Rice, and Hoyt fading channels) can be also easily derived when the average signal-to-noise ratio is sufficiently large, which shows the diversity order and array gain.