Quantum key distribution (QKD) offers a promising solution by providing information-theoretic security based on the principles of quantum mechanics. Beyond theoretical experiments, QKD network construction and verification are actively progressing in various locations worldwide. Continuousvariable QKD (CVQKD) has emerged as a strong candidate for integration into optical networks, particularly due to its compatibility with coherent detection schemes used in existing optical communication systems. Gaussian-modulated (GM) CVQKD enables simpler security analysis through covariance matrices, but its practical implementation typically requires highperformance optical components, leading to increased cost and complexity. In contrast, discrete-modulated (DM) CVQKD using modulation formats, such as quadrature amplitude modulation (QAM), can reduce implementation costs by utilizing the existing optical components. However, its security analysis requires more advanced techniques due to the non-Gaussian nature of the quantum states involved. This study evaluates the performance of GM- and DM-CVQKD under a common optical fiber channel model. Our results show that the secure key rates (SKRs) of DM-CVQKD with probabilistic constellation shaping (PCS) 64QAM and PCS-256QAM drop below zero at transmission distances of 277 km and 399 km, respectively. The results confirm the feasibility of DM-CVQKD for long-distance secure communication over optical fiber networks when appropriate modulation formats and PCS are employed.
Quantum key distribution (QKD) offers a promising solution by providing information-theoretic security based on the principles of quantum mechanics. Beyond theoretical experiments, QKD network construction and verification are actively progressing in various locations worldwide. Continuousvariable QKD (CVQKD) has emerged as a strong candidate for integration into optical networks, particularly due to its compatibility with coherent detection schemes used in existing optical communication systems. Gaussian-modulated (GM) CVQKD enables simpler security analysis through covariance matrices, but its practical implementation typically requires highperformance optical components, leading to increased cost and complexity. In contrast, discrete-modulated (DM) CVQKD using modulation formats, such as quadrature amplitude modulation (QAM), can reduce implementation costs by utilizing the existing optical components. However, its security analysis requires more advanced techniques due to the non-Gaussian nature of the quantum states involved. This study evaluates the performance of GM- and DM-CVQKD under a common optical fiber channel model. Our results show that the secure key rates (SKRs) of DM-CVQKD with probabilistic constellation shaping (PCS) 64QAM and PCS-256QAM drop below zero at transmission distances of 277 km and 399 km, respectively. The results confirm the feasibility of DM-CVQKD for long-distance secure communication over optical fiber networks when appropriate modulation formats and PCS are employed.
Quantum key distribution (QKD) enables the establishment of secret keys between users connected via a channel vulnerable to eavesdropping, with information-theoretic security, that is, independently of the power of a malevolent party [1]. QKD systems based on the encoding of the key information on continuous variables (CV), such as the values of the quadrature components of coherent states [2], [3], present the major advantage that they only require standard telecommunication technology. However, the most general security proofs for CVQKD required until now the use of Gaussian modulation by the transmitter, complicating practical implementations [4]–[6]. Here, we experimentally implement a protocol that allows for arbitrary, Gaussian-like, discrete modulations, whose security is based on a theoretical proof that applies generally to such situations [7]. These modulation formats are compatible with the use of powerful tools of coherent optical telecommunication, allowing our system to reach an estimated performance of tens of megabit per second secret key rates over 25 km
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
We propose a discrete-modulation continuous-variable quantum key distribution protocol based on coherent-state quadrature amplitude modulation combined with probabilistic amplitude shaping. Designed to overcome the practical limitations of Gaussian modulation schemes, the proposed protocol employs finite-energy shaped constellations and enables efficient implementation using standard telecom components while retaining compatibility with homodyne detection and reverse reconciliation. Assuming a linear quantum channel model, characterized by a linear input–output relation between quadratures, and considering collective attacks in the asymptotic regime, we evaluate the secret key rate, achievable transmission distance, optimal launch power, and excess noise tolerance for different constellation sizes, comparing the results with those of the benchmark GG02 protocol. Our results show that probabilistic shaping significantly enhances the performance of discrete-modulation schemes, allowing high-order constellations to closely approach the performance of GG02 in terms of secret key rate, transmission distance, optimal launch power, and excess noise tolerance while preserving practical implementability. By leveraging mature coherent optical communication technologies, the proposed approach provides a realistic pathway toward experimentally feasible high-rate continuous-variable quantum key distribution systems.
Continuous Variables Quantum Key Distribution (CV-QKD) tackles the problem of the generation and distribution of cryptographic keys without assuming any computational limitations while employing standard telecom equipment. Gaussian Modulation (GM) theoretically maximizes the information a CV-QKD system is capable of transmitting while exhibiting a higher resistance to excess channel noise. However, GM-CV-QKD protocols put an extreme burden on the transmitter’s random number source and tend to be more susceptible to imperfect state preparation. Due to these difficulties, most experimental implementations of CV-QKD have used Discrete Modulation (DM). The closer the DM constellation approaches a GM one, the closer the theoretical performance of the associated system will be to the optimum value. To achieve this, high-cardinality constellations, coupled with probabilistic shaping, can be explored. However, choosing a too complex constellation will cause the modulation stage imperfections to again become apparent. Thus, the choice of the constellation format is not direct and is of high importance. In this work we present a methodology to determine the optimum constellation for a given DM-CV-QKD system, taking into account the limitations of the modulation stage, choosing from a variety of M-QAM and M-APSK constellations coupled with probabilistic shaping. Our obtained methodology will allow for the optimum modulation format for each specific system to be selected.
Compared with discrete variable quantum key distribution (DVQKD), continuous variable (CV) QKD has high security bit rate and other advantages, which, however, are slightly insufficient in secure transmission distance. In addition, the application of quantum catalysis has significantly improved the performance of Gaussian modulated (GM) CVQKD, especially in secure transmission distance. Recently, the application of quantum catalysis has significantly improved the performance of GM-CVQKD. However, whether it can be used to improve the performance of discrete modulated (DM) CVQKD protocol is still ambiguous. Therefore, a scheme of DM CVQKD protocol based on quantum catalysis is proposed in this paper to further improve the performance of the proposed protocol in terms of secure key rate, secure transmission distance and maximum tolerable noise. Our results show that under the same parameters, when the transmittance T introduced by quantum catalysis is optimized, the proposed scheme can effectively further improve the performance of QKD system compared with the original four-state modulation CVQKD scheme. In particular, when the tolerable excess noise is 0.002, the use of quantum catalysis can break the safe communication distance of 300 km with a key rate of 10–8 bits/pulse. However, if this noise is too large, the improvement in the effect of quantum catalysis on protocol performance will be restrained. In addition, in order to highlight the advantages of the use of quantum catalysis, the ultimate limit PLOB (Pirandola-Laurenza-Ottaviani-Banchi) bound of point-to-point quantum communication is given in this paper. The simulation results indicate that although neither the original scheme nor the proposed scheme can break the bound, compared with the former, the latter can be close to the boundary in long-distance transmission. These results provide theoretical basis for achieving the ultimate goal of global quantum security communication.
Continuous-variable quantum key distribution is a compelling framework for scalable quantum networks due to its seamless integration with existing optical communication infrastructure. However, a fundamental gap persists between theoretical protocols requiring ideal Gaussian modulation and the constrained, discrete-modulated signals dictated by practical high-speed hardware. Current security proofs for discrete modulation rely on semidefinite programming, which suffers from prohibitive computational overhead for high-order constellations and lacks direct physical insight into non-Gaussian modulation.In this Letter, we overcome this limitation by developing a security framework that obviates semidefinite programming in favor of an approach grounded fundamentally in the Heisenberg uncertainty principle. By introducing a multi-mode entanglement-source model to characterize non-Gaussian state preparation, we establish an explicit mapping between constellation geometry and the secret key rate. This framework effectively quantifies the security implications of hardware-limited, finite state preparation, enabling both numerical and analytical security analysis under high-order constellations. We experimentally validate our method on both discrete-component and integrated photonic platforms, demonstrating that a quadrature amplitude modulation format with 256 constellation points can asymptotically approach the Gaussian capacity limit. Beyond quantum key distribution, the principle of tightening uncertainty-constrained bounds via source-mode expansion offers a paradigm for exploring the information-theoretic properties of complex non-Gaussian systems.