Continuous-variable Quantum Key Distribution Research Articles

Artificial key fingerprints for continuous-variable quantum key distribution

Artificial key fingerprints for continuous-variable quantum key distribution

Secret key rate of continuous-variable quantum key distribution with finite codeword length

Secret key rate of continuous-variable quantum key distribution with finite codeword length

Free space continuous variable Quantum Key Distribution with discrete phases

Quantum Key Distribution (QKD) offers unconditional security in principle. Many QKD protocols have been proposed and demonstrated to ensure secure communication between two authenticated users. Continuous variable (CV) QKD offers many advantages over discrete variable (DV) QKD since it is cost-effective, compatible with current classical communication technologies, efficient even in daylight, and gives a higher secure key rate. Keeping this in view, we demonstrate a discrete modulated CVQKD protocol in the free space which is robust against polarization drift. We also present the simulation results with a noise model to account for the channel noise and the effects of various parameter changes on the secure key rate. These simulation results help us to verify the experimental values obtained for the implemented CVQKD.

Measurement-device-independent continuous variable quantum key distribution protocol operation in optical transport networks

Measurement-device-independent continuous variable quantum key distribution protocol operation in optical transport networks

High-Performance Intermediate-Frequency Balanced Homodyne Detector for Local Local Oscillator Continuous-Variable Quantum Key Distribution

In the continuous-variable quantum key distribution (CV-QKD) system with a local local oscillator (LLO), the center frequency of the sender and the receiver’s source are not exactly the same and a certain frequency drift exists over time, resulting in the frequency of the signal received near the intermediate frequency. Therefore, the LLO system needs an intermediate-frequency balanced homodyne detector (BHD), which needs better symmetry of the arms of the BHD, to obtain the less-common mode noise. Moreover, the traditional intermediate-frequency receiver in classical communication is not available in the CV-QKD system because of the low quantum-to-classical noise ratio. In view of this, in this paper, we construct a broadband intermediate-frequency BHD based on ratio frequency and integrated circuit technology, whose bandwidth can exceed 270 MHz and whose quantum-to-classical noise ratio can reach 14.9 dB. Meanwhile, the BHD has an excellent linear performance with a gain of 22.4 k. By adopting our intermediate-frequency BHD, the secret key rate of the pilot-sequential Gaussian modulated coherent state CV-QKD system with an LLO can reach over 430.8 kbps of 60 km at the standard fiber length, which paves the way to achieve a high-performance LLO CV-QKD system with intermediate-frequency BHD.

Practical continuous-variable quantum key distribution with feasible optimization parameters

Continuous-variable quantum key distribution (CV-QKD) offers an approach to achieve a potential high secret key rate (SKR) in metropolitan areas. There are several challenges in developing a practical CV-QKD system from the laboratory to the real world. One of the most significant points is that it is really hard to adapt different practical optical fiber conditions for CV-QKD systems with unified hardware. Thus, how to improve the performance of practical CV-QKD systems in the field without modification of the hardware is very important. Here, a systematic optimization method, combining the modulation variance and error correction matrix optimization, is proposed to improve the performance of a practical CV-QKD system with a restricted capacity of postprocessing. The effect of restricted postprocessing capacity on the SKR is modeled as a nonlinear programming problem with modulation variance as an optimization parameter, and the selection of an optimal error correction matrix is studied under the same scheme. The results show that the SKR of a CV-QKD system can be improved by 24% and 200% compared with previous frequently used optimization methods theoretically with a transmission distance of 50 km. Furthermore, the experimental results verify the feasibility and robustness of the proposed method, where the achieved optimal SKR achieved practically deviates <1.6% from the theoretical optimal value. Our results pave the way to deploy high-performance CV-QKD in the real world.

Experimental upstream transmission of continuous variable quantum key distribution access network.

Continuous variable quantum key distribution that can be implemented using only low-cost and off-the-shelf components reveals great potential in practical large-scale realization. Access networks, as a modern network necessity, connect many end-users to the network backbone. In this work, we first demonstrate upstream transmission quantum access networks using continuous variable quantum key distribution. A two-end-user quantum access network is then experimentally realized. Through phase compensation, data synchronization, and other technical upgrades, we achieve a secret key rate of the total network of 390 kbits/s. In addition, we extend the case of a two-end-user quantum access network to the case of a multiplicity of users, and analyze the network capacity in the case of a multiplicity of users by measuring the additive excess noise from different time slots.

Impact of transmitter imbalances on the security of continuous variables quantum key distribution

Continuous-variable quantum key distribution (CV-QKD) provides a theoretical unconditionally secure solution to distribute symmetric keys among users in a communication network. However, the practical devices used to implement these systems are intrinsically imperfect, and, as a result, open the door to eavesdropper attacks. In this work, we study the impact of transmitter stage imperfections on the performance and security of a Discrete Modulated (DM) CV-QKD system using M-symbol Quadrature Amplitude Modulation (M-QAM) and Amplitude and Phase Shift Keying (M-APSK) coupled with Probabilistic Constellation Shaping (PCS). Assuming two different modulation stage topologies, we first deform the constellations and then evaluate the secure key rate achievable with the deformed constellation. The presented results show that, due to the erroneously estimated channel parameters, non-monitored imbalances greatly reduce the system’s performance, with situations where Bob and Alice estimate that no secure bits can be obtained while the real value of the key rate is still positive. Our results show the importance of monitoring these constellation imbalances and show that the optimal constellation may vary depending on the degree of device imperfection.

Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel.

Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.

Denial-of-Service Attack Defense Strategy for Continuous Variable Quantum Key Distribution via Deep Learning

In the practical Continuous Variable Quantum Key Distribution (CVQKD) system, there is a large gap between the ideal theoretical model and the actual physical system. There are still some inevitable flaws, which give quantum hackers the opportunity to manipulate the channel in complex communication environments and launch Denial of Service attacks on the quantum channel. Therefore, a DoS attack-aware defense scheme for the CVQKD system based on convolutional neural networks (CNN) is proposed. The simulation results show that the proposed model can effectively detect DoS attacks launched by quantum hackers in CVQKD system in a complex communication environment, and the model has strong robustness due to the addition of the attention mechanism module. In addition, multiple sets of comparative experiments show that compared with the existing artificial neural network model, the CNN-based model has higher accuracy and stability.

Parameter estimation calibration of discretized polar modulation continuous-variable quantum key distribution.

In experimental setups of continuous-variable quantum key distribution (CV-QKD), the ideal Gaussian modulation will suffer from discretization and degrade into discretized polar modulation (DPM), which deteriorates the accuracy of parameter estimation and results in an overestimation of excess noise. We demonstrate that in the asymptotic case, the DPM-induced estimation bias is determined exclusively by the modulation resolutions and can be modeled as a quadratic function. To obtain an accurate estimation, a calibration on the estimated excess noise is implemented based on the closed-form expression of the quadratic bias model, while statistical analysis of the model residuals defines the upper bound of estimated excess noise and the lower bound of secret key rate. Simulation results show that when modulation variance is 25 and excess noise is 0.02, the proposed calibration scheme can eliminate an estimation bias of 14.5%, thus enhancing the efficiency and feasibility of DPM CV-QKD.

Subcarrier wave continuous-variable quantum key distribution with Gaussian modulation: composable security analysis

In this paper, we continue the study of the quantum cryptographic GG02 protocol, performed using the approach based on the subcarrier waves. We modify the scheme via heterodyne detection and perform security analysis for the full trusted hardware noise model in the presence of collective attacks with finite-key effects. It is shown that the system can potentially distribute the key even if the level of losses in the channel is above 9 dB. This result is consistent with the general technical level and comply with modern standards of practical CV-QKD systems. Finally, the system under consideration fully meets the criterion of composability.

Effects of experimental impairments on the security of continuous-variable quantum key distribution

Quantum Key Distribution (QKD) is a cutting-edge communication method that enables secure communication between two parties. Continuous-variable QKD (CV-QKD) is a promising approach to QKD that has several advantages over traditional discrete-variable systems. Despite its potential, CV-QKD systems are highly sensitive to optical and electronic component impairments, which can significantly reduce the secret key rate. In this research, we address this challenge by modeling a CV-QKD system to simulate the impact of individual impairments on the secret key rate. The results show that laser frequency drifts and small imperfections in electro-optical devices such as the beam splitter and the balanced detector have a negative impact on the secret key rate. This provides valuable insights into strategies for optimizing the performance of CV-QKD systems and overcome limitations caused by component impairments. By offering a method to analyze them, the study enables the establishment of quality standards for the components of CV-QKD systems, driving the development of advanced technologies for secure communication in the future.

Adversarial Perturbation Elimination with GAN Based Defense in Continuous-Variable Quantum Key Distribution Systems

Machine learning is being applied to continuous-variable quantum key distribution (CVQKD) systems as defense countermeasures for attack classification. However, recent studies have demonstrated that most of these detection networks are not immune to adversarial attacks. In this paper, we propose to implement typical adversarial attack strategies against the CVQKD system and introduce a generalized defense scheme. Adversarial attacks essentially generate data points located near decision boundaries that are linearized based on iterations of the classifier to lead to misclassification. Using the DeepFool attack as an example, we test it on four different CVQKD detection networks and demonstrate that an adversarial attack can fool most CVQKD detection networks. To solve this problem, we propose an improved adversarial perturbation elimination with a generative adversarial network (APE-GAN) scheme to generate samples with similar distribution to the original samples to defend against adversarial attacks. The results show that the proposed scheme can effectively defend against adversarial attacks including DeepFool and other adversarial attacks and significantly improve the security of communication systems.

Non-Gaussian Reconciliation for Continuous-Variable Quantum Key Distribution

Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV QKD). For Gaussian-modulated coherent-state CV QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multiedge-type low-density parity-check codes (MET LDPC) are used in a non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error-correction performance of Gaussian data and non-Gaussian data. The results show that the error-correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50 % for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25 %.

High-performance long-distance discrete-modulation continuous-variable quantum key distribution.

We experimentally demonstrate a high-rate discretely modulated continuous-variable quantum key distribution over 80-km standard single-mode fiber with a 2.5 Gbaud, 16-symbol, two-ring constellation. With the help of well-designed digital signal processing algorithms, the excess noise of the system can be effectively suppressed. The achieved secret key rates are 49.02 Mbits/s, 11.86 Mbits/s, and 2.11 Mbits/s over 25-km, 50-km, and 80-km optical fiber, respectively, and achieve 67.4%, 70.0%, and 66.5% of the secret key rate performance of a Gaussian-modulated protocol. Our work shows that it is feasible to build a high-performance, long-distance continuous-variable quantum key distribution system with only a small constellation size.

Rate-Adaptive Polar-Coding-Based Reconciliation for Continuous-Variable Quantum Key Distribution at Low Signal-to-Noise Ratio

Information reconciliation significantly impacts the performance of the practical continuous-variable quantum key distribution (CV QKD) system. Fixed-rate error-correction codes limit the potential applications of the CV QKD because they lead to reduced reconciliation efficiency when the signal-to-noise ratio of the quantum channel changes, further deteriorating the system's performance. Therefore, we propose a rate-adaptive polar-coding-based reconciliation scheme for practical CV QKD systems with the time-variant quantum channel. Experimental results verify that the proposed scheme can successfully extract secret keys within the range of signal-to-noise ratios from $\ensuremath{-}0.5$ to $\ensuremath{-}4.5$ dB, and the minimum frame-error rate can be less than ${10}^{\ensuremath{-}3}$. Moreover, the proposed scheme can promote the application of the CV QKD system in a realistic environment.

Experimental Demonstration of LLO Continuous-Variable Quantum Key Distribution With Polarization Loss Compensation

The compensation process for the state of polarization (SOP) from quantum signal plays an important role in the practical implementation of continuous-variable quantum key distribution (CV-QKD). In contrast to the previous scheme using an expensive digital dynamic polarization controller, we choose a cheaper manual polarization controller interfaced with a digital algorithm based on Kalman filter to achieve compensation of the polarization loss under the condition that the SOP of the fiber is relatively stable. This paper also enumerates the details of other digital signal processing method to achieve final secret key rate. And a pilot-sequential Gaussian modulated coherent state (GMCS) continuous-variable quantum key distribution system with a local local oscillator (LLO) is experimentally implemented based on the analysis of excess noise. Finally, the experimental results show that the method of polarization loss compensation takes advantages in maintaining the stability of the final secret key rate. And a secret key rate of 110 kbps is achieved within 20 km optical fiber (with 4 dB loss) under the finite-size block of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1 \times {10^{6}}$</tex-math></inline-formula> during a more extended time in the laboratory.

Continuous-mode quantum key distribution with digital signal processing

Continuous-variable quantum key distribution (CVQKD) offers the specific advantage of sharing keys remotely by the use of standard telecom components, thereby promoting cost-effective and high-performance metropolitan applications. Nevertheless, the introduction of high-rate spectrum broadening has pushed CVQKD from a single-mode to a continuous-mode region, resulting in the adoption of modern digital signal processing (DSP) technologies to recover quadrature information from continuous-mode quantum states. However, the security proof of DSP involving multi-point processing is a missing step. Here, we propose a generalized method of analyzing continuous-mode state processing by linear DSP via temporal modes theory. The construction of temporal modes is key in reducing the security proof to single-mode scenarios. The proposed practicality oriented security analysis method paves the way for building classical compatible digital CVQKD.

Sub-Mbps key-rate continuous-variable quantum key distribution with local local oscillator over 100-km fiber.

We experimentally demonstrated a sub-Mbps key rate Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) over a 100-km transmission distance. To efficiently control the excess noise, the quantum signal and the pilot tone are co-transmitted in the fiber channel based on wideband frequency and polarization multiplexing methods. Furthermore, a high-accuracy data-assisted time domain equalization algorithm is carefully designed to compensate the phase noise and polarization variation in low signal-to-noise ratio. The asymptotic secure key rate (SKR) of the demonstrated CV-QKD is experimentally calculated to be 7.55 Mbps, 1.87 Mbps, and 0.51 Mbps over a transmission distance of 50 km, 75 km, and 100 km, respectively. The experimentally demonstrated that the CV-QKD system significantly improves the transmission distance and SKR compared to the state-of-art GMCS CV-QKD experimental results, and shows the potential for long-distance and high-speed secure quantum key distribution.