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.
Highlights
Quantum communication provides a promising solution to break the Shannon channel capacity limit [1] and achieve an unprecedented level of security [2] simultaneously, two competing tasks which cannot be realized in conventional technologies [3]
Further investigation and real application of quantum key distribution (QKD) did not attract much attention until it was proved that the quantum computer was able to break public-key cryptosystems, which are commonly used in the modern cryptography [6], [7]
In real commercial QKD implementations, a single-photon mechanism is typically used to convey the information, and the corresponding common detection scheme is called single photon avalanche photodiodes (SPADs) where the SPAD diode is operated in Geiger mode to count single-photons [24]
Summary
Quantum communication provides a promising solution to break the Shannon channel capacity limit [1] and achieve an unprecedented level of security [2] simultaneously, two competing tasks which cannot be realized in conventional technologies [3]. The authors in [31] first investigated the performance of received powers at both the legitimate receiver and eavesdropper in FSO QKD systems with taking random pointing errors into account, and derived the closed-form expressions for the corresponding average received powers. Similar to [37]–[39], the transmission probability in this paper is defined as the probability that the received power is satisfied one or more pre-set thresholds in the FSO QKD system, which is obviously a natural variant of the outage probability in traditional communications [35] Motivated by observing those facts outlined above, we investigate the performance of QKD systems over FSO links in terms of transmission probabilities depending on three different conditions. Exact closed-form expressions in Rayleigh, Hoyt and Rice cases (three special cases of the Beckmann distribution) for the transmission probability depending only on the legitimate receiver are given.
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