Continuous-variable quantum secret sharing (CVQSS) based on discrete modulation is a viable alternative to Gaussian-modulated CVQSS due to its implementation simplicity. However, its theoretical performance remains far below the Gaussian-modulated counterparts. In this work we propose a CVQSS scheme based on constellation shaping, which enables near-Gaussian modulation effects by combining probabilistic and geometric constellation shaping with quadrature amplitude modulation (QAM). For the probabilistic shaping, binomial distribution and Boltzmann-Maxwell (BM) distribution are selected to adjust the occurrence probabilities of quantum states, and for the geometric shaping, triangular quadrature amplitude modulation (TQAM) is employed to optimize the geometric positions of the constellation points. Numerical simulations indicate that compared with other discrete-modulated CVQSS schemes, the proposed BM-distributed 16-TQAM scheme achieves the highest asymptotic secret key rate and the lowest detection error probability. Moreover, the optimal modulation variance of this scheme is higher than that of other schemes, demonstrating that the players can employ a larger modulation variance when preparing coherent states, thereby enhancing the signal-to-noise ratio of the whole system and providing a potential advantage in long-distance transmission.
Continuous-variable quantum secret sharing (CVQSS) based on discrete modulation is a viable alternative to Gaussian-modulated CVQSS due to its implementation simplicity. However, its theoretical performance remains far below the Gaussian-modulated counterparts. In this work we propose a CVQSS scheme based on constellation shaping, which enables near-Gaussian modulation effects by combining probabilistic and geometric constellation shaping with quadrature amplitude modulation (QAM). For the probabilistic shaping, binomial distribution and Boltzmann-Maxwell (BM) distribution are selected to adjust the occurrence probabilities of quantum states, and for the geometric shaping, triangular quadrature amplitude modulation (TQAM) is employed to optimize the geometric positions of the constellation points. Numerical simulations indicate that compared with other discrete-modulated CVQSS schemes, the proposed BM-distributed 16-TQAM scheme achieves the highest asymptotic secret key rate and the lowest detection error probability. Moreover, the optimal modulation variance of this scheme is higher than that of other schemes, demonstrating that the players can employ a larger modulation variance when preparing coherent states, thereby enhancing the signal-to-noise ratio of the whole system and providing a potential advantage in long-distance transmission.
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.
We propose a continuous-variable quantum secret sharing scheme based on multi-ring discrete modulation, which we called MR-CVQSS. In this scheme, phase shift keying (PSK)-modulated coherent states are allowed to be further discretely modulated with different amplitudes, so that these modulated coherent states can be scattered on different amplitude rings in phase space. The advantage for this multi-ring structure is that the error probability of quantum detector for discriminating discretely-modulated coherent states (DMCSs) is more lower than that of original single-ring discretely modulated CVQSS, which is beneficial for improving the performance of whole CVQSS system. We derive the security bound for MR-CVQSS against both eavesdroppers and dishonest users, and the numerical simulation shows that the performance of MR-CVQSS in terms of both maximal transmission distance and maximal available number of users can be largely improved. Moreover, security analysis shows that the modulation variance of MR-CVQSS does not need to be very small, thereby improving the signal-to-noise ratio (SNR) of whole CVQSS system.
Abstract In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme (MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol. We conduct a comprehensive analysis of the improved protocol’s performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.
Abstract Continuous-variable quantum secure direct communication (CVQSDC) with Gaussian modulation (GM) demands a considerable quantity of random numbers during the preparation process and encodes them separately on the quadrature components of the quantum states. Hence, high-speed random number generators are required to satisfy this demand, which is difficult to implement in practical applications. CVQSDC with discrete modulation (DM), correspondingly, employs a finite number of quantum states to achieve encoding, which can circumvent the shortcomings of the GM scheme. Based on the advantages of DM, the issue of attaining the most optimal secrecy capacity and communication distance remains to be resolved. Here, we propose a CVQSDC protocol based on N-symbol amplitude phase shift keying (N-APSK), which exploits the Boltzmann–Maxwell distribution assisted probability shaping technique. In comparison with the uniform distribution, according to 32-APSK CVQSDC, the proposed scheme extends the communication distance by about 38%, while obtaining a higher secrecy capacity at the same communication distance. Furthermore, increasing the value of N will concurrently increase the quantity of rings in the constellation, thereby facilitating enhancements of communication distance. This work incorporates the modulation approaches prevalently employed in classical communication into the realm of quantum communication, attaining gratifying advancements in communication distance and secrecy capacity, and concurrently facilitating the integrated development of quantum communication and classical communication.
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.
A quantum noise stream cipher scheme (QNSC) based on triangular quadrature amplitude modulation (TQAM) and the secret probabilistic shaping (SPS) is studied. Compared with rectangular quadrature amplitude modulation (QAM), TQAM is a more compact symmetrical structure, which results in better transmission performance and greater noise masking number. Then, SPS is realized, where the probabilistic shaping information as the secret key is masked into noise and transmitted with the encrypted signal simultaneously. The combination of SPS and QNSC makes it impossible for an attacker to obtain the ciphertext, which enhances the security of QNSC scheme without introducing additional key. TQAM and probabilistic shaping improve the transmission performance of QNSC scheme. Under 7% forward error correction (FEC) threshold in back-to-back system, compared with QAM/QNSC systems, TQAM/QNSC provides an OSNR gain of ∼ 0.6 dB, and SPS-TQAM/QNSC provides an OSNR gain of ∼ 1.2 dB. The proposed scheme is demonstrated with the net data rate of 34.28 Gbit/s over 140 km single-span standard single mode fiber.