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.
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.
Endogenous security in next-generation wireless communication systems attracts increasing attentions in recent years. A typical solution to endogenous security problems is the Quantum Key Distribution (QKD), where unconditional security can be achieved thanks to the inherent properties of quantum mechanics. Continuous Variable-Quantum Key Distribution (CV-QKD) enjoys high Secret Key Rate (SKR) and good compatibility with existing optical communication infrastructure. Traditional CV-QKD usually employ coherent receivers to detect coherent states, whose detection performance is restricted to the standard quantum limit. In this paper, we employ a generalized Kennedy receiver called CD-Kennedy receiver to enhance the detection performance of coherent states in turbulent channels, where Equal-Gain Combining (EGC) method is used to combine the output of CD-Kennedy receivers. Besides, we derive the SKR of a post-selection based CV-QKD protocol using both CD-Kennedy receiver and homodyne receiver with EGC in turbulent channels. We further propose an equivalent transmittance method to facilitate the calculation of both the Bit-Error Rate (BER) and SKR. Numerical results show that the CD-Kennedy receiver can outperform the homodyne receiver in turbulent channels in terms of both BER and SKR performance. We find that BER and SKR performance advantage of CD-Kennedy receiver over homodyne receiver demonstrate opposite trends as the average transmittance increases, which indicates that two separate system settings should be employed for communication and key distribution purposes. Besides, we also demonstrate that the SKR performance of a CD-Kennedy receiver is much robust than that of a homodyne receiver in turbulent channels.
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.
We experimentally demonstrate an eight-state continuous-variable quantum key distribution (CV-QKD) over atmospheric turbulence channels. The high secret key rate (SKR) is enabled by 4-D multiplexing of 96 channels, i.e., six-channel wavelength-division multiplexing, four-channel orbital angular momentum multiplexing, two-channel polarization multiplexing, and two-channel spatial-position multiplexing. The atmospheric turbulence channel is emulated by a spatial light modulator on which a series of azimuthal phase patterns yielding Andrews' spectrum are recorded. A commercial coherent receiver is implemented at Bob's side, followed by a phase noise cancellation stage, where channel transmittance can be monitored accurately and phase noise can be effectively eliminated. Compared to four-state CV-QKD, eight-state CV-QKD protocol potentially provides a better performance by offering higher SKR, better excess noise tolerance, and longer secure transmission distance. In our proposed CV-QKD system, the minimum transmittances of 0.24 and 0.26 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission. A maximum SKR of 3.744 Gb/s is experimentally achievable, while a total SKR of 960 Mb/s can be obtained in case of mean channel transmittances.
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 is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.