Performance Analysis of QKD-based Terrestrial FSO System using QPSK under Atmospheric Turbulence

This work analyzes a terrestrial-based free-space quantum key distribution system employing quadrature-phase shift keying signaling (QKD-QPSK). An analytical framework is proposed to determine various joint probabilities under the gamma-gamma turbulence channel model without utilizing the Gaussian–Laguerre (GL) method. Although GL-based method provides ease of computation of integral forms, but it is not always stable. Using derived joint probabilities, novel analytical expressions for the probability of sifted keys (P
sift
), quantum bit error rate (QBER), error probability for the eavesdropper (P
eve
), and the ergodic secret-key rate (ESKR) are determined for QKD-QPSK system. This work also reveals that the QKD-QPSK system can be transformed into QKD-based binary phase-shift keying (QKD-BPSK) system. Furthermore, using the proposed analytical framework, all the considered performance metrics are also evaluated for the QKD-BPSK system. Finally, QKD-QPSK and QKD-BPSK systems are compared under moderate and strong turbulence regimes. Comparative results indicate that QKD-QPSK outperforms QKD-BPSK in terms of P
eve
. However, QKD-BPSK is superior to QKD-QPSK for P
sift
and QBER. Furthermore, a positive ESKR can be achieved for both systems with the proper selection of threshold coefficient (ρ) and transmitted power (P
t
).