Dual-Protection for Free-Space Quantum Key Distribution: Enhancing Security Against Eve via Channel Randomness

This paper proposes a novel quantum key distribution (QKD) set-up designed to enhance the security of a free-space optical (FSO) quantum communication system. By incorporating channel ordering information, the proposed QPSK-QKD (P-QPSK-QKD) system leverages the inherent randomness of FSO channels, providing dual protection against eavesdroppers (Eve). The first layer of security is achieved through the QPSK-QKD mechanism, while the second arises from the randomness of the FSO channels. To ensure a comprehensive investigation, the performance of P-QPSK-QKD and the existing QPSK-QKD (E-QPSK-QKD) system is analyzed using a Málaga distributed atmospheric turbulence channel model incorporating pointing errors. Novel closed-form expressions are derived for different performance metrics, including probability of sifted keys, quantum bit error rate, probability of Eve (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eve</sub>), and ergodic secret key rate (ESKR), under both perfect and imperfect feedback conditions. Intensive examination indicates that, unlike E-QPSK-QKD, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eve</sub> shows a water-falling trend with increasing signal-to-noise ratios (SNR) under dual thresholds, P-QPSK-QKD achieves a saturated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eve</sub>, enhancing security. Moreover, under the single threshold, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eve</sub> of P-QPSK-QKD is twice that of E-QPSK-QKD. Additionally, due to channel randomness, the mutual information between Alice and Eve remains zero (for both single and dual thresholds), even at infinite SNR for P-QPSK-QKD, providing consistently higher ESKR than E-QPSK-QKD system under both perfect and imperfect feedback conditions.