Continuous-variable Quantum Key Distribution System Research Articles

Continuous-variable quantum key distribution over 28.6 km fiber with an integrated silicon photonic receiver chip

Quantum key distribution, which ensures information-theoretically secret key generation, is currently advancing through photonic integration to achieve high performance, cost reduction, and compact size, thereby facilitating the large-scale deployment. Continuous-variable quantum key distribution is an attractive approach for photonic integrations due to its compatibility with off-the-shelf optical communication devices. However, its chip-based systems have encountered significant limitations primarily related to the shot-noise-limited receiver design, which demands low noise, wide bandwidth, high clearance, and well stability. Here, we report the implementation of a real local oscillator continuous-variable quantum key distribution system with an integrated silicon photonic receiver chip. Thanks to the well-designed chip-based homodyne detectors with a bandwidth up to 1.5 GHz and a clearance up to 7.42 dB, the transmission distance of the system has been extended to 28.6 km, achieving a secret key generation rate of Mbps level. This technological advancement enables the quantum key distribution systems with photonic integrated receivers to achieve the coverage in both access network scenarios and short-distance metropolitan interconnections, paving the way for the development of the next-generation quantum key distribution networks on a large scale.

Highly stable power control for chip-based continuous-variable quantum key distribution system.

Quantum key distribution allows secret key generation with information theoretical security. It can be realized with photonic integrated circuits to benefit the tiny footprints and the large-scale manufacturing capacity. Continuous-variable quantum key distribution is suitable for chip-based integration due to its compatibility with mature optical communication devices. However, the quantum signal power control compatible with the mature photonic integration process faces difficulties on stability, which limits the system performance and causes the overestimation of a secret key rate that opens practical security loopholes. Here, a highly stable chip-based quantum signal power control scheme based on a biased Mach-Zehnder interferometer structure is proposed, theoretically analyzed, and experimentally implemented with standard silicon photonic techniques. Simulations and experimental results show that the proposed scheme significantly improves the system stability, where the standard deviation of the secret key rate is suppressed by an order of magnitude compared with the system using traditional designs, showing a promising and practicable way to realize a highly stable continuous-variable quantum key distribution system on chip.

Adjusting Optical Polarization with Machine Learning for Enhancing Practical Security of Continuous-Variable Quantum Key Distribution

An available trick to mitigate the interference of environmental noise in quantum communications is to modulate signals with time-polarization multiplexing. Conversely, due to effects of the atmospheric turbulence in free space, the polarization of signals fluctuates randomly, resulting in feasible information leakage when direct polarization demultiplexing is carried out at the receiver, drowning out the noise-contained signals. For enhancing the practical security of the continuous-variable quantum key distribution (CVQKD), we propose a machine learning (ML) approach for optimization of the dynamic polarization control (DPC) of signals transmitted through atmospheric turbulence. An optimal DPC scheme can be adaptively adjusted with ML algorithms, which is based on the received signals at the receiver for solving the loophole problem of information leakage since it provides an accurate response to the polarization changes regarding the anamorphic signals. The performance of the CVQKD system can be increased in terms of secret key rates and maximal transmission distance as well. Numerical simulation shows the positive effect of the ML-based DPC while taking into account the secret key rate of the CVQKD system. The ML-based DPC effectively reduces the feasibility of information leakage and hence results in an increased secret key rate of the practical CVQKD system.

Continuous-variable quantum key distribution system: Past, present, and future

Quantum key distribution provides secure keys with information-theoretic security ensured by the principle of quantum mechanics. The continuous-variable version of quantum key distribution using coherent states offers the advantages of its compatibility with telecom industry, e.g., using commercial laser and homodyne detector, is now going through a booming period. In this review article, we describe the principle of continuous-variable quantum key distribution system; focus on protocols based on coherent states, whose systems are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. We start by reviewing the theoretical protocols and the current security status of these protocols. Then, we discuss the system structure, the key module, and the mainstream system implementations. The advanced progresses for future applications are discussed, including the digital techniques, system on chip, and point-to-multipoint system. Finally, we discuss the practical security of the system and conclude with promising perspectives in this research field.

Continuous-variable quantum key distribution robust against environmental disturbances.

Continuous variable quantum key distribution (CV-QKD) can guarantee that two parties share secure keys even in the presence of an eavesdropper. However, the polarization direction of the coherent state transmitted in CV-QKD is susceptible to environmental disturbances during channel transmission, making it difficult to share keys consistently over long periods of time. Therefore, a CV-QKD system that can resist environmental disturbance is very urgent. In this paper, we propose a new optical architecture for CV-QKD based on the Faraday-Michelson interference (FMI) structure, and finally form an all-single-mode (SM) fiber-based stable CV-QKD system which employs transmitted local oscillator (TLO) scheme and discrete modulation coherent state (DMCS) protocol. Specifically, since the Faraday mirror rotates the polarization direction of light by 90o, the birefringence effect of light can be effectively dealt with, thus ensuring the same polarization state of light before and after reflection. The final simulation results show that the theoretical secret key rate of this scheme can reach 139 kbps at 70 km, which can further improve the stability and robustness of CV-QKD in the real environment, and provide technical support for the next-generation high-stability QKD system.

Low-complexity adaptive reconciliation protocol for continuous-variable quantum key distribution

In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol gives a reconciliation efficiency higher than 98.1% in the SNR below −20 dB and maintains a certain SKR in long-distance transmission.

A Novel Continuous-Variable Quantum Key Distribution Scheme Based on Multi-Dimensional Multiplexing Technology

Dual-polarization division multiplexing (DPDM) is considered to be a potential method to boost the secure key rate (SKR) of the continuous-variable quantum key distribution (CV-QKD) system. In this article, we propose a pilot alternately assisted local local oscillator (LLO) CV-QKD scheme based on multi-dimensional multiplexing, where time division multiplexing and frequency division multiplexing are combined with dual-polarization multiplexing techniques to dramatically isolate the quantum signal from the pilot tone. We establish a general excess noise model for the LLO CV-QKD system to analyze the influence mechanism of various disturbances (e.g., time-domain diffusion, frequency-domain modulation residual, and polarization perturbation) on the key parameters, such as the channel transmittance and excess noise. Specifically, the photon leakage noise from the reference path to the quantum path and that between quantum signals with two different polarization paths are simultaneously analyzed in the dual-polarization LLO CV-QKD scheme for the first time. Furthermore, a series of simulations are established to verify the performance of the proposed scheme. The results show that the maximal isolation degree achieves 84.0 dB~90.4 dB, and the crosstalk between pilot tones and quantum signals can be suppressed to a very small range. By optimizing the system parameters (e.g., modulation variance and repetition frequency), the SKR with 12.801 Mbps@25 km is achieved under the infinite polarization extinction ratio (PER) and 30 dB residual ratio of the frequency modulation in the nanosecond-level pulse width. Moreover, the performance of the proposed DPDM CV-QKD scheme under relatively harsh conditions is simulated; the results show that the SKR with 1.02 Mbps@25 km is achieved under a relatively low PER of 17 dB with the nanosecond-level pulse width and 20 dB residual ratio of the frequency modulation. Our work lays an important theoretical foundation for the practical DPDM LLO CV-QKD system.

Four-state discrete modulation continuous variable quantum key distribution based on hardware synchronization

<sec>In the case of continuous-variable quantum key distribution (CV-QKD) systems, synchronization is a key technology that ensures that both the transmitter and receiver obtain corresponding data synchronously. By designing an ingenious time sequence for the transmitter and receiver and using the peaking value acquisition technique and time domain heterodyne detection, we experimentally realize a four-state discrete modulation CV-QKD with a repetition rate of 10 MHz, transmitting over a distance of 25 km. With well-designed time sequence of hardware, Alice and Bob can obtain corresponding data automatically without using numerous software calculation methods.</sec><sec>The secure key rates are calculated by using the method proposed by the Lütkenhaus group at the University of Waterloo in Canada. In the calculation, we first estimate the first and the second moment by using the measured quadratures of displaced thermal states, followed by calculating the secret key rate by using the convex optimization method through the reconstruction of the moments. There is no need to assume a linear quantum transmission channel to estimate the excess noise. Finally, secure key rates of 0.0022—0.0091 bit/pulse are achieved, and the excess noise is between 0.016 and 0.103.</sec><sec>In this study, first, we introduce the prepare-and-measure scheme and the entanglement-based scheme of the four-state discrete modulation protocol. The Wigner images of the four coherent states on Alice’s side, and four displaced thermal states on Bob’s side are presented. Second, the design of hardware synchronization time series is introduced comprehensively. Third, the CV-QKD experiment setup is introduced and the time sequence is verified. Finally, the calculation method of secure key rate using the first and the second moment of quadrature is explained in detail. The phase space distribution of quadratures is also presented. The secret key rate ranges between 0.0022 and 0.0091 bits/pulse, and the equivalent excess noise are between 0.016 and 0.103. The average secret key bit rate is 24 kbit/s. During the experiment, the first and the second moment of the quantum state at the receiver end are found to fluctuate owing to the finite-size effect. This effect reduces the value of the secure key rate and limits the transmission distance of the CV-QKD system.</sec><sec>In conclusion, four-state discrete modulation CV-QKD based on hardware synchronization is designed and demonstrated. The proposed hardware synchronization method can effectively reduce the cost, size, and power consumption. In the future, the finite-size effect will be investigated theoretically and experimentally to improve the performance of system.</sec>

Robust frame synchronization for continuous-variable quantum key distribution with coherent states.

In a practical continuous variable quantum key distribution (CVQKD) system, frame synchronization is crucial for its operation, especially in conditions of low signal-to-noise ratio (SNR) and phase drift. This paper introduces a robust frame synchronization scheme for CVQKD systems that only utilizes quantum signals. The proposed scheme effectively employs randomly selected segments of quantum signals to achieve frame synchronization, eliminating the need for additional modulation. The performance of this scheme applied in a local local oscillator scenario is thoroughly analyzed through numerical simulations. The results demonstrate that the proposed scheme is capable of withstanding low SNR and arbitrary slow phase drift, as well as fast phase drift originates from two independent lasers, while also slightly improving the secret key rate compared to the scheme using inserted synchronization frames. These findings validate the feasibility of implementing the proposed scheme for long-distance CVQKD in practical scenarios.

Simple and Fast Polarization Tracking Algorithm for Continuous-Variable Quantum Key Distribution System Using Orthogonal Pilot Tone

To reduce the influence of random channel polarization variation, especially fast polarization perturbation, for continuous-variable quantum key distribution (CV-QKD) systems, a simple and fast polarization tracking algorithm is proposed and experimentally demonstrated. The algorithm is implemented by an orthogonal pilot tone scheme, one of the pilot tones is used for estimating the polarization rotation angle, and the other one is used for compensating the polarization perturbation introduced phase noise. Meanwhile, residual effects are compensated precisely with the help of a real-valued FIR filter. In this case, the excess noise introduced by polarization perturbation is effectively suppressed. Experimental results show that the polarization scrambling rate ≥12.57 krad/s can be tracked by using the proposed algorithm, and a good estimated parameters performance is achieved. Compared to conventional polarization tracking algorithms such as the constant modulus algorithm (CMA), experimental results show that the polarization tracking capability of the proposed algorithm is significantly improved. Furthermore, much faster polarization tracking performance is evaluated by digital simulations, and the simulation results show that about 188.50 Mrad/s can be tracked by the proposed algorithm. Thus, our method provides effective technology for the practical application of fiber-based CV-QKD.

Reconciliation Efficiency Impact on Discrete Modulated CV-QKD Systems Key Rates

Continuous variable quantum key distribution (CV-QKD) allows the distribution of symmetric keys in a secure manner. CV-QKD systems can extract keys at its maximum rate when using Gaussian modulation (GM). Nonetheless, GM demands high-capacity random number sources and tends to be very hard to approach in practice. To circumvent these disadvantages, higher-order probabilistic -shaped discrete modulation (DM) can be used. State-of-the-art works compute the key rates of DM-CV-QKD systems considering a fixed value for the reconciliation efficiency and do not take into account the frame error rate (FER) of the system, thus over or under estimating the key rates. In this work, we study the security bounds of CV-QKD systems considering probabilistic shaped DM formats with 256-symbols in the finite-size regime. This accounting for the true value of the reconciliation efficiency, and the FER of the information reconciliation step. Both conventional and hexagonal 256-quadrature amplitude modulation (QAM) constellations yield higher key rates than 256-amplitude and phase shift keying (APSK) constellations, with 256-QAM constellations being indistinguishable in performance with GM for high transmission distances. Minimum signal-to-noise ratio (SNR) values were fixed from a FER analysis through a CV-QKD simulation allowing for key extraction considering different FER levels. Lower FER values are associated with higher SNRs in the system and thus lower achievable transmission distances. Nonetheless, the FER maximizing the extraction key rate is not null. Our results show that the extraction key rate is maximized by SNR adjustment which should have in account both the reconciliation efficiency and the FER.

Silicon photonics-integrated time-domain balanced homodyne detector for quantum tomography and quantum key distribution

We designed and experimentally demonstrated a silicon photonics-integrated time-domain balanced homodyne detector (TBHD), containing an optical part of dimensions of 1.5 mm × 0.4 mm. To automatically and accurately balance the detector, new variable optical attenuators were used, and a common mode rejection ratio of 86.9 dB could be achieved. In the quantum tomography experiment, the density matrix and Wigner function of a coherent state were reconstructed with 99.97% fidelity. The feasibility of this TBHD in a continuous-variable quantum key distribution (CVQKD) system was also demonstrated. Our TBHD technologies are expected to be used in silicon photonics-integrated CVQKD system and silicon photonics-integrated BB84 heterodyne system.

High-speed information reconciliation with syndrome-based early termination for continuous-variable quantum key distribution.

Information reconciliation (IR) is an indispensable component in the post-processing stage of continuous-variable quantum key distribution (CV-QKD), which adopts error-correcting codes to address the asymmetry of secret keys. Currently, low-density parity-check (LDPC) decoding in IR is a post-processing bottleneck in high-speed CV-QKD systems since the upper bound on secret key rate is higher than the information throughput delivered by decoder. In this paper, we study the relationship between the syndrome variation pattern (SVP) in iterative decoding and reconciliation frame error rate. An early termination scheme based on SVP is proposed and applied to multidimensional reconciliation, which can increase information throughput by adaptively adjusting the iteration number of iterative decoding to real-time decoding status. Furthermore, we show that only the resulting syndrome of the highest-rate code part in Raptor-like LDPC codes needs to be calculated to verify whether the reconciliation is successful by studying the convergency of resulting syndrome, which can save a large fraction of computational resources for syndrome calculation. Simulation results show that information throughput of the proposed scheme can be improved by 617.1% compared to the existing scheme when the IR efficiency reaches 97.09%. The proposed scheme points out a new direction for breaking the post-processing bottleneck in high-speed CV-QKD systems.

Adversarial Attack Defense Method for a Continuous-Variable Quantum Key Distribution System Based on Kernel Robust Manifold Non-Negative Matrix Factorization

Machine learning has been applied in continuous-variable quantum key distribution (CVQKD) systems to address the growing threat of quantum hacking attacks. However, the use of machine learning algorithms for detecting these attacks has uncovered a vulnerability to adversarial disturbances that can compromise security. By subtly perturbing the detection networks used in CVQKD, significant misclassifications can occur. To address this issue, we utilize an adversarial sample defense method based on non-negative matrix factorization (NMF), considering the nonlinearity and high-dimensional nature of CVQKD data. Specifically, we employ the Kernel Robust Manifold Non-negative Matrix Factorization (KRMNMF) algorithm to reconstruct input samples, reducing the impact of adversarial perturbations. Firstly, we extract attack features against CVQKD by considering the adversary known as Eve. Then, we design an Artificial Neural Network (ANN) detection model to identify these attacks. Next, we introduce adversarial perturbations into the data generated by Eve. Finally, we use the KRMNMF decomposition to extract features from CVQKD data and mitigate the influence of adversarial perturbations through reconstruction. Experimental results demonstrate that the application of KRMNMF can effectively defend against adversarial attacks to a certain extent. The accuracy of KRMNMF surpasses the commonly used Comdefend method by 32.2% and the JPEG method by 30.8%. Moreover, it exhibits an improvement of 20.8% compared to NMF and outperforms other NMF-related algorithms in terms of classification accuracy. Moreover, it can complement other defense strategies, thus enhancing the overall defensive capabilities of CVQKD systems.

Suppression of Fading Noise in Satellite-Mediated Continuous-Variable Quantum Key Distribution via Clusterization

The satellite-mediated continuous-variable quantum key distribution (CV-QKD) protocol, which relies on off-the-shelf telecommunication components, has the potential for a global quantum communication network with all-day operation. However, the transmittance fluctuation of satellite-mediated links leads to the arriving quantum state showing non-Gaussian property, introducing extra fading noise in security analysis and limiting the secret key rate of the protocol. Here, we consider the clusterization method for data post-processing to suppress the fading noise in both downlink and uplink scenarios, where the measurement data are divided into several clusters, and we perform security analysis separately. In particular, we set the optimal upper and lower bounds of each cluster in terms of the probability distribution of transmittance (PDT), while finding an optimal cluster number for the trade-off between fading noise and the composable finite-size effect. Numerical analysis shows that the proposed method can improve the composable finite-size rate when the fading noise is large enough, even with only two clusters. Moreover, a high-speed CV-QKD system with a higher frequency of signal preparation and detection can extend the proposed method to work in the case of lower fading noise.

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.

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.

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.

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.