This letter proposes a novel modulation signaling-based quantum key distribution (QKD) protocol that employs eight phases of the optical carrier, therefore named octa-phase shift keying QKD (8PSK-QKD). The proposed QKD protocol shares two key bits simultaneously and consequently exhibits increased spectral efficiency compared to existing modulation signaling-based QKD protocols. Different performance metrics, viz., probability of sifted keys ($P _{\text{sift}}$), quantum bit error rate, probability of sifted keys of Eve, and Eve’s error probability ($P _{\text{eve}}$), are determined using a novel analytical framework for a free-space optical channel under the combined effect of atmospheric turbulence and pointing error. To inspect the potential of the system, the 8PSK-QKD system is compared with the quadrature phase shift keying-based QKD (QPSK-QKD) and subcarrier intensity modulation binary phase shift keying-based QKD (SIM/BPSK-QKD) systems. Numerical results reveal that the 8PSK-QKD system follows the criteria of an acceptable QKD system even with transmitting two key bits at a time. Additionally, the 8PSK-QKD system outperform the SIM/BPSK-QKD and QPSK-QKD by offering better$P _{\text{sift}}$and$P _{\text{eve}}$.
This letter proposes a novel modulation signaling-based quantum key distribution (QKD) protocol that employs eight phases of the optical carrier, therefore named octa-phase shift keying QKD (8PSK-QKD). The proposed QKD protocol shares two key bits simultaneously and consequently exhibits increased spectral efficiency compared to existing modulation signaling-based QKD protocols. Different performance metrics, viz., probability of sifted keys (Psift), quantum bit error rate, probability of sifted keys of Eve, and Eve’s error probability (Peve), are determined using a novel analytical framework for a free-space optical channel under the combined effect of atmospheric turbulence and pointing error. To inspect the potential of the system, the 8PSK-QKD system is compared with the quadrature phase shift keying-based QKD (QPSK-QKD) and subcarrier intensity modulation binary phase shift keying-based QKD (SIM/BPSK-QKD) systems. Numerical results reveal that the 8PSK-QKD system follows the criteria of an acceptable QKD system even with transmitting two key bits at a time. Additionally, the 8PSK-QKD system outperform the SIM/BPSK-QKD and QPSK-QKD by offering betterPsiftandPeve.
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 (Psift), quantum bit error rate (QBER), error probability for the eavesdropper (Peve), 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 Peve. However, QKD-BPSK is superior to QKD-QPSK for Psiftand QBER. Furthermore, a positive ESKR can be achieved for both systems with the proper selection of threshold coefficient (ρ) and transmitted power (Pt).
This paper proposes a novel two-way free-space quantum key distribution (QKD) protocol, which can be implemented using standard free-space optical (FSO) systems with subcarrier intensity-modulation (SIM) binary phase-shift-keying (BPSK) and direct-detection (DD) receiver. Different eavesdropping threats, including unauthorized receiver, beam-splitting, and intercept-resend attacks, are considered in the security analysis of the proposed protocol. Under the constraints on security requirements, we analytically investigate the design criteria for transmitter and receiver, in particular, the intensity modulation depth at the transmitter and the dual-threshold setting of the receiver in two-way free-space QKD systems. Quantum bit error rate (QBER), the ergodic secret-key rate, and the probability of detecting eavesdropper of the proposed system are analytically derived in closed-form expressions, considering the atmospheric loss, turbulence, and receiver noises.
This paper proposes a novel free-space quantum key distribution (QKD) system using subcarrier intensity-modulation (SIM) binary phase-shift-keying (BPSK) and dual-threshold/direct-detection (DT/DD) receiver with an avalanche photodiode (APD). The proposed system enables the adoption of well-developed analytical models in conventional free-space optical (FSO) communications and achieves the QKD function with a simple configuration. We analytically investigate the design criteria for transmitter and receiver, in particular, the modulation depth and the setting for dual-threshold in the context of security requirement of QKD systems. The quantum bit error rate (QBER) and the ergodic secret-key rate of the proposed system are analytically derived in closed-form expressions, considering the channel loss, atmospheric turbulence modeled by the log-normal distribution, and receiver noises. Monte-Carlo (M-C) simulations are also implemented to validate the analytical results, and numerical results confirm the feasibility of the proposed system.
This work proposes and analyzes quadrature-phase shift keying (QPSK)-assisted quantum key distribution (QPSK-QKD) for indoor visible light communication (VLC) systems. The joint probabilities are calculated for QPSK-QKD system to determine analytical expressions for the probability of sifted keys (Psift), quantum bit error rate (QBER), error probability for the eavesdropper (Peve), and ergodic secret key rate. As a special case of QPSK-QKD, the binary phase-shift keying-assisted QKD (BPSK-QKD) system is also examined in terms of considered performance metrics. Comparative results of QPSK-QKD and BPSK-QKD systems indicate that BPSK-QKD outperforms QPSK-QKD in terms of Psiftand QBER. However, QPSK-QKD is superior to BPSK-QKD for Peve. Finally, it is concluded that based on the requirement, a choice can be made between QPSK-QKD and BPSK-QKD for a VLC system.
This paper proposes a novel design and analyzes security performance of quantum key distribution (QKD) protocol over free-space optics (FSO). Unlike conventional QKD protocols based on physical characteristics of quantum mechanics, the proposed QKD protocol can be implemented on standard FSO systems using subcarrier intensity modulation binary phase shift keying and direct detection with a dual-threshold receiver. Under security constraints, the design criteria for FSO transmitter and receiver, in particular, the modulation depth and the selection of dual-threshold detection, respectively, is analytically investigated. For the security analysis, quantum bit error rate, ergodic secret-key rate, and final key-creation rate are concisely derived in novel closed-form expressions in terms of finite power series, taking into account the channel loss, atmospheric turbulence-induced fading, and receiver noises. Furthermore, Monte-Carlo simulations are performed to verify analytical results and the feasibility of the proposed QKD protocol.
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 (Peve), and ergodic secret key rate (ESKR), under both perfect and imperfect feedback conditions. Intensive examination indicates that, unlike E-QPSK-QKD, wherePeveshows a water-falling trend with increasing signal-to-noise ratios (SNR) under dual thresholds, P-QPSK-QKD achieves a saturatedPeve, enhancing security. Moreover, under the single threshold,Peveof 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.