Continuous-variable quantum key distribution (CV-QKD) suffers from significant secret key rate (SKR) limitations in long-haul transmission. Existing hardware-oriented capacity boosting approaches are hindered by prohibitive costs and intricate system architectures. To address these challenges, this paper proposes a time-domain unitary precoding scheme to enhance the SKR by making full use of the non-flat noise frequency spectrum inherent to practical CV-QKD systems. This paper derives an analytical expression for the optimal precoder when only excess or electronic noise is colored and employs the Riemann Conjugate Gradient (RCG) algorithm for iterative optimization when both types of noise are colored. Numerical simulations demonstrate that, for a 40 km transmission link with both colored excess noise and electronic noise, the optimized scheme attains a 1.07 to 5.6 fold SKR improvement compared to conventional CV-QKD systems.
Continuous-variable quantum key distribution (CV-QKD) suffers from significant secret key rate (SKR) limitations in long-haul transmission. Existing hardware-oriented capacity boosting approaches are hindered by prohibitive costs and intricate system architectures. To address these challenges, this paper proposes a time-domain unitary precoding scheme to enhance the SKR by making full use of the non-flat noise frequency spectrum inherent to practical CV-QKD systems. This paper derives an analytical expression for the optimal precoder when only excess or electronic noise is colored and employs the Riemann Conjugate Gradient (RCG) algorithm for iterative optimization when both types of noise are colored. Numerical simulations demonstrate that, for a 40 km transmission link with both colored excess noise and electronic noise, the optimized scheme attains a 1.07 to 5.6 fold SKR improvement compared to conventional CV-QKD systems.
Passive optical network (PON)-based continuous-variable quantum key distribution (CV-QKD) enables an optical line terminal (OLT) to establish multiple information-theoretically secure keys with optical network units (ONUs) over untrusted quantum channels. However, the average secret key rate (SKR) of PON systems is severely constrained by heterogeneous channel conditions among ONUs. Hardware-based solutions for PON systems, such as wavelength-division multiplexing and multi-core fiber, are also burdened by prohibitive costs and implementation complexity. Conventional signal-processing approaches that rely solely on power regulation are suboptimal for CV-QKD because the SKR exhibits a non-monotonic dependence on the channel transmit power. Although unitary precoding can effectively enhance the SKR of point-to-point links by exploiting the inherently non-flat noise frequency spectrum of practical CV-QKD systems, extending this technique to multi-user PONs introduces unique challenges: all users share a single global transmit power budget and a common precoding matrix, thereby requiring joint optimization to maximize the average SKR. To address these challenges, we propose what we believe is a novel time-domain precoding scheme that integrates precoding with power loading and jointly optimizes the unitary precoding matrix and power allocation profile by exploiting the inherently non-flat noise frequency spectrum of practical CV-QKD systems. Numerical simulations demonstrate that, for a standard 20 km link with 64 ONUs, the proposed scheme improves the SKR by factors of 2.52 to 4.57 over conventional unoptimized systems and by factors of 1.02 to 1.90 over PON systems employing a discrete Fourier transform (DFT) precoding matrix with optimized power loading.
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 proposed orthogonal-frequency-division-multiplexing (OFDM) CV-QKD protocol, we demonstrate a high-rate multi-carrier (MC) CV-QKD with a 10 GHz symbol rate that achieves Gbps SKR within 10 km and Mbps SKR over 100 km in the finite-size regime under composable security against collective attacks. The results are achieved by suitable optimization of subcarrier number and modulation variance, well-controlled excess noise induced by both the OFDM mechanism and the efficient DSP scheme, and high-performance post-processing capacity realized by the heterogeneous computing scheme. The composable finite-size SKR reaches 1779.45 Mbps@5 km, 1025.49 Mbps@10 km, 370.50 Mbps@25 km, 99.93 Mbps@50 km, 25.70 Mbps@75 km, and 2.25 Mbps@100 km, which improves the SKR by two orders of magnitude and quintuples the maximal transmission distance compared to the most recently reported CV-QKD results [ Nat. Commun. 13 , 4740 ( 2022 ) NCAOBW 2041-1723 10.1038/s41467-022-32161-y ]. 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 toward future high-speed quantum metropolitan and access networks.
In previous continuous-variable quantum key distribution (CV-QKD) systems, the transmission rate is limited by the Nyquist criterion. Since the data symbols transmit without intersymbol interference (ISI) under this limitation, how to improve the secret key rate is still a notoriously hard problem. Faster-than-Nyquist (FTN) technology has been viewed as a potential technique in future communication systems, because of its higher spectrum efficiency and faster symbol rate. In this paper, a CV-QKD system based on FTN is proposed. The transmission of an FTN system is simulated, and then we analyze the Mazo limit and the constrained capacities of the system, and finally compare the secret key rate of FTN signals and Nyquist signals. Our proposed scheme is especially beneficial for the high-speed scenario. Simulation results demonstrate that such a CV-QKD system can increase channel capacity and enhance key rate; it can also improve the safe transmission distance of CV-QKD.
Quantum key distribution (QKD) can provide secret keys with security rooted in quantum mechanics, but operation alongside high-capacity classical traffic remains limited by the excess-noise budget of weak quantum states in conventional solid-core fiber. Here, we combine ultralow-loss anti-resonant hollow-core fiber with residual-carrier-assisted discrete-modulation continuous-variable QKD (DM-CV-QKD) to address both propagation-induced coexistence noise and low-SNR phase recovery. Over a 24.3-km hollow-core link with 3.3-dB end-to-end loss, a dual-polarization 15-Gbaud DM-CV-QKD channel achieves an average asymptotic secret-key rate (SKR) of 153.22 Mb/s and a finite-size SKR of 149.99 Mb/s, while 39 coherent wavelength-division-multiplexed channels deliver an aggregate data rate of 7.6 Tb/s and a net data rate of 7.2 Tb/s. The system can even sustain a positive SKR under a high classical launch power of up to 15 dBm, without an optical bandpass filter (BPF). Finite-size analysis against collective attacks further yields a projected positive secret-key rate at a 100-km-equivalent condition. These results show that an anti-resonant hollow-core fiber, combined with carrier-assisted phase recovery, can greatly extend the operating regime of shared-fiber quantum-secured coherent links, pointing to a promising approach for integrating high-rate CV-QKD with high-capacity optical networks.
Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication technologies. However, as CV-QKD systems progress toward digital implementations, device nonidealities drive the optical field from a single-mode to a continuous-mode region, thereby underscoring the mismatch between theoretical models and practical systems. Here, we introduce temporal modes to construct an entanglement-based scheme that more accurately captures device nonidealities and develop a corresponding secret key rate calculation method applicable to continuous-mode scenarios. We demonstrate that optimizing the pulse-shaping format can significantly improve performance under detector-bandwidth-limited conditions. Experimental results also confirm that the proposed model effectively describes the impact of sampling-time deviations. We further analyze a linear weighted-reconstruction digital signal processing method,which improves the secret key rate by approximately 50% in a 30-km fiber experiment without requiring additional hardware, demonstrating a substantial performance enhancement at metropolitan distances. The proposed theoretical framework accommodates a broader range of experimental conditions and can guide the optimization of digital CV-QKD systems.
Abstract Quantum key distribution (QKD) is one quantum technology that can provide secure encryption keys for data transmission. The secret key rate (SKR) is a core performance indicator in QKD, which directly determines the transmission rate of enciphered data. Here, for the first time, we demonstrate a high-key-rate Gaussian-modulated continuous-variable QKD (CV-QKD) using telecom optical components. The framework of CV-QKD over these components is constructed. Specifically, the high-rate low-noise Gaussian modulation of coherent states is realized by a classical optical IQ modulator. High-baud low-intensity quantum signals are received by an integrated coherent receiver under the shot-noise limit. A series of digital signal processing algorithms are proposed to achieve accurate signal recovery and key distillation. The system can yield a high asymptotic SKR of 10.37 Mbps within 20 km standard telecom fiber, and the secure distance can exceed 100 km. This result confirms the feasibility of CV-QKD with state-of-the-art performance using telecom optical components. Besides, due to the ease of integrating these discrete components, it provides a high-performance and miniaturized QKD solution for the metropolitan quantum network.