Abstract Continuous-variable quantum key distribution (CV-QKD) relies on the local oscillator (LO) not only as the phase reference for coherent detection but also as the basis for shot-noise unit (SNU) calibration in parameter estimation. In practical implementations, random LO intensity fluctuations distort the SNU normalization and thus bias the estimation of channel transmittance and excess noise, leading to inaccurate secret-key-rate evaluation. In this paper, we propose a passive LO-monitoring assisted parameter-estimation method for Gaussian-modulated coherent-state (GMCS) CV-QKD protocol. In the proposed scheme, the SNU is calibrated once using the average LO intensity before key distribution, while the LO fluctuation variance is monitored in real time through a passive monitoring branch. By incorporating the monitored fluctuation information into the parameter-estimation model, the bias induced by LO intensity fluctuations can be compensated without resorting to active real-time SNU calibration. Numerical simulations show that the proposed method yields estimated secret key rates close to those obtained under ideal LO conditions and significantly outperforms the conventional non-real-time SNU calibration method when the LO fluctuations become pronounced. The method provides a simple and practical way to improve the robustness and reliability of GMCS CV-QKD systems.

We experimentally demonstrated a high-performance multi-protocol continuous-variable quantum key distribution (CV-QKD) using one transceiver. The demonstrated multi-protocol CV-QKD system can simultaneously distribute 5 subcarriers with Gaussian, 4QAM, 16QAM, 64QAM, and 1024QAM modulation protocols based on orthogonal-frequency-division-multiplexing (OFDM) technology. Moreover, the modulation variance and probability distribution factor of 5 subcarriers are carefully optimized to maximize their respective SKRs. Besides, we innovatively design an effective OFDM-based DSP scheme and a precise dual-stage phase noise compensation scheme to realize a low excess noise for each subcarrier operating at a 2 GHz symbol rate. Thus, the multi-protocol CV-QKD achieves multiple SKRs of 48.79, 7.58, 23.67, 32.93, and 36.78 Mbps over a typical transmission distance of 50 km within a single transmission. Therefore, our work provides a practical solution to achieve highly efficient, interoperable, flexible, and secure QKDs for high-speed quantum secure communication.

Discrete modulation is a practical and device-friendly solution for high-speed continuous-variable quantum key distribution (CV-QKD), offering strong compatibility with existing coherent optical communication systems. However, its achievable transmission distance has remained considerably shorter than that of Gaussian-modulated protocols, limiting its practical deployment. In this work, we overcome this limitation by combining an advanced security analysis method with probabilistically shaped modulation and an efficient digital signal processing algorithm. We experimentally demonstrate a local local oscillator CV-QKD system over a 126.56 km span of single-mode fiber, achieving an asymptotic secret key rate of 171.42 kbps. This result significantly extends the reach of discrete-modulated CV-QKD and confirms its potential as a viable candidate for the commercialization and large-scale practical application of quantum key distribution technology. Discrete modulation offers a practical approach for high-speed transmission in continuous-variable quantum key distribution (CV-QKD) but struggles with limited transmission distances. The authors employ advanced security analysis, sophisticated signal processing algorithms, and probabilistic shaping to achieve a record 126.56 km transmission distance, supporting the commercial viability of CV-QKD systems

Quantum key distribution (QKD), providing a way to generate secret keys with information-theoretic security,is arguably one of the most significant achievements in quantum information. The continuous-variable QKD (CV-QKD) offers the potential advantage of achieving a higher secret key rate (SKR) within a metro area, as well as being compatible with the mature telecom industry. However, the SKR and transmission distance of state-of-the-art CV-QKD systems are currently limited. Here, based on the novelly proposed orthogonal-frequency-division-multiplexing (OFDM) CV-QKD protocol, we demonstrate for the first time a high-rate multi-carrier (MC) CV-QKD with a 10 GHz symbol rate that chieves Gbps SKR within 10km and Mbps SKR over 100 km in the finite-size regime under composable security against collective attacks. The record-breaking results are achieved by suitable optimization of subcarrier number and modulation variance, well-controlled excess noise induced by both OFDM mechanism and efficient DSP scheme, and high-performance post-processing capacity realized by heterogeneous computing scheme. The composable finite-size SKR reaches 1779.45 Mbps@5km, 1025.49 Mbps@10km, 370.50 Mbps@25km, 99.93 Mbps@50km, 25.70 Mbps@75km,and 2.25 Mbps@100km, which improves the SKR by two orders of magnitude and quintuples the maximal transmission distance compared to most recently reported CV-QKD results [Nature Communications, 13, 4740 (2022)]. Interestingly, it is experimentally verified that the SKR of the proposed MC CV-QKD can approach five times larger than that of the single-carrier CV-QKD with the same symbol rate without additional hardware costs. Our work constitutes a critical step towards future high-speed quantum metropolitan and access networks.

Quantum key distribution can provide information-theoretical secure communication, which is now heading towards building the quantum secure network for real-world applications. In most built quantum secure networks, point-to-multipoint (PTMP) topology is one of the most popular schemes, especially for quantum access networks. However, due to the lack of custom protocols with high secret key rate and compatible with classical optical networks for PTMP scheme, there is still no efficient way for a high-performance quantum access network with a multitude of users. Here, we report an experimental demonstration of a high-rate 16-nodes quantum access network based on passive optical network, where a high-efficient coherent-state PTMP protocol is novelly designed to allow independent secret key generation between one transmitter and multiple receivers concurrently. Such accomplishment is attributed to a well-designed real-time shot-noise calibration method, a series of advanced digital signal processing algorithms and a flexible post-processing strategy with high success probability. Finally, the experimental results show that the average secret key rate is around 2.086 Mbps between the transmitter and each user, which is two orders of magnitude higher than previous demonstrations. With the advantages of low cost, excellent compatibility, and wide bandwidth, our work paves the way for building practical PTMP quantum access networks, thus constituting an important step towards scalable quantum secure networks.

We experimentally demonstrate a high-performance multi-carrier CV-QKD system with asymptotic SKRs of 1819.32Mbps@5km, 1078.48Mbps@10km, 374.19Mbps@25km, 112.96Mbps@50km, 34.63Mbps@75km and 12.58Mbps@100km, marking the first CV-QKD achieving Gbps SKR within 10km and ten Mbps SKR over 100km.

A quantum access network with Mbps level key rate and simple structure compatible with classical network facilities is reported, where the average secret key rate per user can reach 4.24 Mbps at 30 km.

Continuous-variable quantum key distribution (CV-QKD) with plug-and-play design offers a promising route in simplifying the system implementation and shows intriguing prospects for quantum access network applications. However, such a scheme makes it possible for the eavesdropper (Eve) to completely control the source, helping her to gain more information since the laser travels through the unsecured channel before being modulated, which will severely compromise the performance of the system and limit its potential application. To fight against the security loophole, we propose a passive source monitoring scheme based on a combination of beam splitter and homodyne detector, as well as source noise suppression. The corresponding entanglement-based model is established to estimate the secret key rate for the proposed scheme. We show that the performance of the plug-and-play CV-QKD system can be significantly improved by using the source monitoring scheme compared with the untrusted source model. With typical parameters, the maximum transmission distance can be promoted by more than 50%, and the secret key rate can be increased by more than 25% when the transmission distance is longer than 50 km. This study provides a feasible approach for improving the security and performance of the plug-and-play CV-QKD and holds positive potential for practical applications.

In this paper, we propose a multi-rate and multi-protocol CV-QKD scheme based on the orthogonal- frequency-division-multiplexing (OFDM) technology. The proposed OFDM-based multi-carrier CVQKD scheme only requires one transmitter and one receiver to realize QKD with different modulation protocols and different key rates in one communication. More importantly, the multiple subcarriers with different modulation protocols have different excess noise tolerances in the same transmission channel, which can achieve the flexible QKD service even in long-distance and high-disturbance fiber channel. In order to verify the proposed scheme, 5 subcarriers with QPSK, 64QAM, 256QAM, 1024QAM and Gaussian modulation protocols are evaluated by the SDP and no-switch Gaussian security analysis method at different transmission distances. The simulation results show the proposed OFDM-based multi-carrier scheme allows various QKDs with different modulation protocols and different key rates in one communication. Moreover, according to the obtained 5 SKRs, we can choose the optimal modulation protocol of the subcarriers to meet different needs of quantum network operators. In addition, the scheme also can choose much more subcarriers and different symbol rates to flexibly achieve the QKD in different quantum secure communication scenarios. Therefore, the proposed scheme changes the modulation protocol, subcarrier number and symbol rate to achieve the interoperability, flexibility and compatibility.

In this article, we propose a time and orthogonal polarization division multiplexing scheme for local local oscillator continuous-variable quantum key distribution (LLO CV-QKD) system. According to the influence mechanism of time-domain diffusion and polarization disturbance on the key parameters, such as the channel transmittance and excess noise, of the studied system, we established a dual-polarization theoretical model and verified its validity by simulations. Here, the pulse width at the nanosecond level and polarization extinction ratio (PER) are considered for optimizing the performance of secure key rate (SIKR) quantitatively. For transmitting over 25 km optical fiber, the required PER should be above 22 dB when the pulse width is fixed to lns. Moreover, the optimal repetition frequency is obtained. In this case, 5.25 Mbps SKR can be achieved under the lns pulse width and 25dB PER, considering the $10^{11}$ finite-size block. Our work provides a systematic and theoretical framework for the study of improving the SKR of the dual-polarization CV-QKD system.

Quantum access network with 8 nodes and a secret key rate of over 6 Mbps per user is firstly demonstrated using passive optical distribution network facilities, paving the way of high-performance and scalable quantum-secured network.

We experimentally demonstrated a sub-Mbps key rate Gaussian-modulated coherent-state continuous-variable quantum key distribution (CV-QKD) over 100 km transmission distance. To efficiently control the excess noise, the quantum signal and the pilot tone are co-transmitted in fiber channel based on wide-band 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 evaluated to be 10.36 Mbps, 2.59 Mbps, and 0.69 Mbps over transmission distance of 50 km, 75 km, and 100 km, respectively. The experimental demonstrated CV-QKD system significantly improves 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.

In this article, we propose a pilot alternately assisted scheme of orthogonal dual-polarization and time multiplexing for the local local oscillator continuous-variable quantum key distribution (LLO CV-QKD). Our scheme utilizes time multiplexing and dual-polarization multiplexing techniques to dramatically isolate the quantum signal from the pilot light. To analyze the influence mechanism of time-domain diffusion and polarization perturbation on the key parameters, such as the channel transmittance and excess noise, of the studied system, a general LLO excess noise model based on polarization extinction ratio (PER) and time-domain pulse extinction ratio (TER) is established. We mainly focus on the photon-leakage noise from the reference path to the quantum signal path, which is first analyzed in the dual polarization LLO regime. Furthermore, we conduct a series of simulations to verify the proposed dual polarization and time multiplexing model. Results show that it maintains a low level of excess noise and a secure key rate (SKR) of 10.25 Mbps@25km can be obtained under the finite-size effect. We achieved 0.93Mbps@25km SKR under a relatively low PER of 17 dB in the nanosecond level pulse width. Our work greatly extends the application scenarios of the dual-polarization division multiplexing CV-QKD system and provides a theoretical and representative framework for the study of improving the performance of the dual-polarization CV-QKD system.

A simple and fast polarization tracking algorithm for pilot tone-assisted CV-QKD system is demonstrated. Experimental results show that the proposed algorithm can track polarization scrambling rate ≥12.57 krad/s with a good performance.

The source noise in plug-and-play continuous variable quantum key distribution (CV-QKD) system plays a crucial role in determining the secret key rate and transmission distance. In general, the source noise is considered untrusted and fully controlled by Eve, which is because the laser travels through the unsecure channel before being modulated. However, this may overestimate the key information stolen by Eve leading to an underestimation of the key rate share between the legal communication parties. Here, we use a beam-splitter with signal attenuation to model the source noise combined with source monitoring scheme to characterize the source imperfection in the plug-and-play CV-QKD system. We show that the performance of the plug-and-play CV-QKD can be significantly improved under the above scheme compared to the untrusted source model. Our numerical simulation results also show that the plug-and-play CV-QKD with source monitoring has a key generation rate close to that of a trusted source under the same simulation parameters.

In this paper, a multi-carrier Gaussian modulated continuous variable quantum key distribution (CV-QKD) scheme has been proposed based on orthogonal frequency division multiplexing (OFDM) for distributing multiplexing independent secret keys encoded on N subcarriers within a single fiber channel. However, the performance of the system will be significantly influenced by the extra modulation noise in the multi-carrier quantum state preparation. Therefore, a modulation noise model is analyzed in more compact for multi-carrier Gaussian modulated CV-QKD system. Specifically, the gain imbalance and quadrature skew in IQ modulation and the third-order intermodulation effect in N subcarrier modulation are systematically analyzed in the OFDM-based multi-carrier CV-QKD with Gaussian modulation. That is, the IQ imbalance noise and the intermodulation noise are modeled as the modulation noise of the multi-carrier Gaussian modulated CV-QKD system. Moreover, the secure performances of the multi-carrier Gaussian modulated CVQKD are evaluated based on the proposed modulation noise model. Besides, the simulation results show the SKRs are greatly increased by N independent quantum state preparation, which indicates that the multi-carrier CV-QKD system gets rid of the asymptotic SKR limit of single-carrier CV-QKD system for future high-rate CV-QKD deployment in broadband access network.

In this paper, we experimentally demonstrate a 5 GBaud four-state continuous-variable quantum key distribution with digital signal processing. By employing a frequency- and polarization-multiplexing quantum key transceiver, the modulation noise and DAC quantization noise in quantum state preparation, the photo-leakage noise in co-fiber transmission, the detection noise and ADC quantization noise in polarization diversity detection can be effectively reduced for achieving an ultra-low level of excess noise. Moreover, the main polarization variation and phase noise can be accurately compensated by designing a precise digital compensation scheme including the pilot-assisted polarization and phase compensation algorithm and the data-assisted equalized compensation algorithm. Besides, the explicit asymptotic secure key rate is evaluated by using an improved semidefinite programming security analysis method, which achieves a 100 Mbps level of secure key rate within 10 km distance.

A high-rate continuous-variable quantum key distribution (CV-QKD) system based on high-order discrete modulation is experimentally investigated. With the help of the novel system scheme, effective digital signal processing (DSP) algorithms and advanced analytical security proof methods, the transmission results of 5.059 km, 10.314 km, 24.490 km, and 50.592 km are achieved for 1 GBaud optimized quantum signals. Correspondingly, the asymptotic secret key rates (SKRs) are 292.185 Mbps, 156.246 Mbps, 50.491 Mbps, and 7.495 Mbps for discrete Gaussian (DG) 64QAM, and 328.297 Mbps, 176.089 Mbps, 51.304 Mbps, and 9.193 Mbps for DG 256QAM, respectively. Under the same parameters, the achieved SKRs of DG 256QAM is almost same as ideal Gaussian modulation. In this case, the demonstrated high-rate discrete-modulated CV-QKD system has the application potential for high-speed security communication under tens of kilometers.