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Anais de XXXV Simpósio Brasileiro de Telecomunicações e Processamento de Sinais

Practical Non-Gaussian Detection for Enhanced Security in CV-QKD Protocols

Joás Lacerda, Lucas Felipe Bezerra de Melo Oliveira, Alexandre B. Tacla

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) has emerged as a leading protocol for provably secure cryptographic key exchange, leveraging quantum properties of optical signals while remaining compatible with existing telecom infrastructure.In these systems, the receiver's detection capability directly impacts the rate at which cryptographic keys can be generated, making it a critical factor for real-time secure communications.Conventional coherent reception schemes (based solely on Gaussian operations) are fundamentally limited in their ability to distinguish quantum states, performing below the ultimate limit allowed by quantum mechanics.Overcoming this limitation requires non-Gaussian detection strategies, which can approach this theoretical bound and unlock higher key generation rates.In this work, we investigate the optimized displacement receiver (ODR) -a non-Gaussian strategy that combines a signal preprocessing step with photon countingas an alternative to conventional homodyne detection for CV-QKD protocols employing binary phase-shift keying (BPSK) modulation.We evaluate its security performance under realistic conditions by modeling practical detector imperfections such as efficiency loss and noise.Our results show that the ODR achieves higher secret key rates than conventional homodyne detection for all detector efficiencies, at all distances, and across the range of detector noise relevant for practical devices, directly translating into enhanced cryptographic performance and extended transmission range.

DOI
10.14209/sbrt.2026.1571301147

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Continuous-variable quantum key distribution (CV-QKD) has emerged as a leading protocol for provably secure cryptographic key exchange, leveraging quantum properties of optical signals while remaining compatible with existing telecom infrastructure.In these systems, the receiver's detection capability directly impacts the rate at which cryptographic keys can be generated, making it a critical factor for real-time secure communications.Conventional coherent reception schemes (based solely on Gaussian operations) are fundamentally limited in their ability to distinguish quantum states, performing below the ultimate limit allowed by quantum mechanics.Overcoming this limitation requires non-Gaussian detection strategies, which can approach this theoretical bound and unlock higher key generation rates.In this work, we investigate the optimized displacement receiver (ODR) -a non-Gaussian strategy that combines a signal preprocessing step with photon countingas an alternative to conventional homodyne detection for CV-QKD protocols employing binary phase-shift keying (BPSK) modulation.We evaluate its security performance under realistic conditions by modeling practical detector imperfections such as efficiency loss and noise.Our results show that the ODR achieves higher secret key rates than conventional homodyne detection for all detector efficiencies, at all distances, and across the range of detector noise relevant for practical devices, directly translating into enhanced cryptographic performance and extended transmission range.
Continuous variable quantum key distribution (CV-QKD) protocol has drawn much attention due to its compatibility with existing optical communication systems. In this paper, we propose a quaternary modulated CV-QKD protocol using displacement receivers and adopt the post-selection scheme to overcome the ‘3dB limit’. We first establish the model of displacement receiver for discriminating quaternary modulated coherent signals in a realistic situation. The performance of non-adaptive displacement receiver and multi-stage feedforward receiver are both investigated under different noises and device imperfections. To improve the receiver performance, we numerically optimize the displacement operation and check the quantum advantage of the displacement receivers over the classical homodyne detection. Then we analyze the security of the proposed CV-QKD protocol. The secret key rate is derived for both types of displacement receivers under the collective beam splitting attack. We also optimize the transmitted signal photons for different channel transmission efficiencies under practical system constraints. Numerical results shed light on the practical application of displacement receivers in CV-QKD protocols. This includes evaluating the necessity of optimizing the displacement and incorporating the feedforward structure in a displacement receiver according to different practical system limitations. Moreover, under higher channel transmission efficiency and increased receiver noise level, a larger coherent amplitude is required for transmitting signals to attain the maximum secret key rate.
Near-optimal binary coherent state discrimination can be achieved by performing a displacement operation followed by photon detection. This displacement serves as a control parameter that can be tuned to optimize a chosen figure of merit, which makes such receivers attractive beyond state discrimination. Here, we turn this discrimination strategy into a complete continuous-variable quantum key distribution (CV-QKD) protocol based on a binary alphabet of noisy coherent states (displaced thermal states) and displacement receivers. We develop a strategy for estimating the channel parameters with the same displacement receiver, since standard quadrature-based methods do not apply. While a key map can be obtained with on/off detection, we demonstrate that reliable parameter estimation requires photon-number-resolving detection with sufficient resolution. Finite detector resolution underestimates the observed noise and constitutes a potential security loophole, which we quantify and show to be mitigable with modest resolution. We analyze the protocol's security against entangling-cloner collective attacks in the asymptotic regime, for both direct and reverse reconciliation, and show that it can generate secret keys even under noisy state preparation and imperfect detection. Interestingly, we find that the displacement that minimizes the discrimination error probability also performs well for key generation, thus providing a useful and analytically tractable tuning strategy for the CV-QKD receiver. We evaluate the protocol's performance over a range of transmittances and noise parameters, showing that the displacement receiver can outperform conventional homodyne detection in experimentally relevant regimes. Together, our results point to displacement receivers as a promising alternative for CV-QKD implementations.
Security analysis of continuous variable quantum key distribution (CV-QKD) remains a topic of extensive academic investigation. In this work, we propose a coherent-state CV-QKD protocol integrating a displacement-based quantum receiver and post-selection strategies. We establish a framework of the protocol under both individual and collective attacks, incorporating practical constraints such as noises and device imperfections. To enhance performance of the protocol, the postselection strategy and the transmitted signal power are optimized for different channel attenuation levels. Numerical results offer insights into the strategy of employing displacement receivers in CV-QKD protocols, revealing that larger transmitted signal power is required under low channel attenuation or severe receiver-side imperfections and noises to achieve higher the secret key rate.
Continuous variable-quantum key distribution (CV-QKD) based on coherent detection has potential to be a cost-effective solution to deploy secure keys over optical networks. This is due to its compatibility with mature optical communication technologies, such as homodyne and heterodyne detection schemes. Nevertheless, realistic implementations of CV-QKD systems suffer from imperfections in the practical devices used to generate and detect the coherent states. Those imperfections deteriorate the performance of the CV-QKD system and can be exploited by an eavesdropper to steal key information without being detected. In this work, we discuss the impact of practical device imperfections on the excess noise of the CV-QKD and on the achievable transmission distance. We also analyze the impact of detection imperfections on the measurement of the shot noise, and its impact on CV-QKD system security.
Photon subtraction can enhance the performance of continuous-variable quantum key distribution (CV QKD). However, the enhancement effect will be reduced by the imperfections of practical devices, especially the limited efficiency of a single-photon detector. In this paper, we propose a non-Gaussian postselection method to emulate the photon substraction used in coherent-state CV QKD protocols. The virtual photon subtraction not only can avoid the complexity and imperfections of a practical photon-subtraction operation, which extends the secure transmission distance as the ideal case does, but also can be adjusted flexibly according to the channel parameters to optimize the performance. Furthermore, our preliminary tests on the information reconciliation suggest that in the low signal-to-noise ratio regime, the performance of reconciliating the postselected non-Gaussian data is better than that of the Gaussian data, which implies the feasibility of implementing this method practically.