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Towards Secure Coherent-State QKD with Practical Quantum Detection

Shuai Han, Mufei Zhao, Renzhi Yuan, Ziyi Xie, Shaojie Yang

Published Dec 8, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/globecom59602.2025.11432526

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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) 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.
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) using coherent states and heterodyne detection enables secure quantum communication based on technology that has large similarities to coherent optical telecommunication. Yet, practical implementations of coherent receivers used in both technologies encounter device imperfections, which for CV-QKD are often not addressed in security proofs. Here, we present a theoretical framework that rigorously accounts for imperfect heterodyne measurements arising from phase and amplitude imbalances in the coherent (heterodyne) receiver. Focusing on collective attacks, we establish a finite-size security proof that reveals how measurement imperfections limit the distance over which a positive key rate is achievable. To mitigate these effects, we propose a local transformation during classical post-processing. We validate our approach experimentally on a CV-QKD system with an imperfect coherent receiver, underscoring its potential for scalable, cost-effective CV-QKD with photonic integrated receivers in which phase and amplitude imbalances naturally appear through manufacturing tolerances.
Continuous-variable quantum key distribution (CV-QKD) has gathered significant interest for its potential to achieve high secret key rates and seamless integration with existing optical communication infrastructure. State-of-the-art CV-QKD systems primarily use coherent states for simplicity. However, squeezed states of light have been theoretically shown to offer significant advantages, including higher secret key rates, greater resilience to excess noise, and reduced requirements on information reconciliation efficiency. In this work, we experimentally verify these theoretical predictions and propose and demonstrate a practical squeezed-state CV-QKD system based on modern local-local oscillator and digital signal processing techniques. Operating over fiber channels and considering finite-size security against collective attacks, we show the advantages of our system over its coherent-state counterpart. Our work paves the way for squeezed states to become practical resources for quantum key distribution and other quantum information protocols.
Continuous variable-quantum key distribution (CV-QKD) protocols attract increasing attentions in recent years because they enjoy high secret key rate (SKR) and good compatibility with existing optical communication infrastructure. Classical coherent receivers are widely employed in coherent states based CV-QKD protocols, whose detection performance is bounded by the standard quantum limit (SQL). Recently, quantum receivers based on displacement operators are experimentally demonstrated with detection performance outperforming the SQL in various practical conditions. However, potential applications of quantum receivers in CV-QKD protocols under turbulent channels are still not well explored, while practical CV-QKD protocols must survive from the atmospheric turbulence in satellite-to-ground optical communication links. In this paper, we consider the possibility of using a quantum receiver called multi-stage CD-Kennedy receiver to enhance the SKR performance of a quadrature phase shift keying (QPSK) modulated CV-QKD protocol in turbulent channels. We first derive the error probability of the multi-stage CD-Kennedy receiver for detecting QPSK signals in turbulent channels and further propose three types of multi-stage CD-Kennedy receiver with different displacement choices, i.e., the Type-I, Type-II, and Type-III receivers. Then we derive the SKR of a QPSK modulated CV-QKD protocol using the multi-stage CD-Kennedy receiver and post-selection strategy in turbulent channels. Numerical results show that the multi-stage CD-Kennedy receiver can outperform the classical coherent receiver in turbulent channels in terms of both error probability and SKR performance and the Type-II receiver can tolerate worse channel conditions compared with Type-I and Type-III receivers in terms of error probability performance.