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Improved Passive State Preparation–Continuous Variable Quantum Key Distribution Scheme Based on Non-Gaussian Operations

Hao Luo, Yue Wang, Hang Zhang, Jiajia Zhong

Published Apr 27, 2026• 0 citations
Publisher

Abstract

Passive state preparation-continuous variable quantum key distribution (PSP-CVQKD) protocol inherits the advantage of high secret key rate (SKR) of CVQKD, while overcoming the drawback of complex modulation equipment in GMCS-CVQKD. In recent years, it has received extensive attention in the experimental field. Even so, short transmission distance remains its prominent issue. In this paper, a scheme for introducing non-Gaussian operations into PSP-CVQKD in optical fiber links is proposed. We derive the input-output relationship of the system, as well as the calculation formulas for the success probability and SKR, when non-Gaussian operations are introduced at both sides of the channels respectively. The results indicate that the improved PSP-CVQKD scheme is feasible in enhancing the SKR performance and can effectively increase the transmission distance. Our scheme provides beneficial ideas for further in-depth research on non-Gaussian operations and the performance improvement of other PSP-CVQKD protocols.

DOI
10.3390/e28050497

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Passive state preparation-continuous variable quantum key distribution (PSP-CVQKD) protocol inherits the advantage of high secret key rate (SKR) of CVQKD, while overcoming the drawback of complex modulation equipment in GMCS-CVQKD. In recent years, it has received extensive attention in the experimental field. Even so, short transmission distance remains its prominent issue. In this paper, a scheme for introducing non-Gaussian operations into PSP-CVQKD in optical fiber links is proposed. We derive the input-output relationship of the system, as well as the calculation formulas for the success probability and SKR, when non-Gaussian operations are introduced at both sides of the channels respectively. The results indicate that the improved PSP-CVQKD scheme is feasible in enhancing the SKR performance and can effectively increase the transmission distance. Our scheme provides beneficial ideas for further in-depth research on non-Gaussian operations and the performance improvement of other PSP-CVQKD protocols.
The conventional Gaussian-modulated coherent-state quantum key distribution (QKD) protocol requires the sender to perform active modulations based on a true random number generator. Compared with it, the passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) equivalently performs modulations passively by exploring the intrinsic field fluctuations of a thermal source, which offers the prospect of chip integration QKD with low cost. In this paper, we propose and experimentally demonstrate a high-rate PSP-CVQKD scheme within an access-network area using high-bandwidth detectors in a continuous wave encoding and decoding way. By proposing effective methods for suppressing the noises during the PSP process and polarization multiplexing to decrease the photon leakage noises, we realize the high-intensity local oscillator transmission, thereby achieving coherent detection with high efficiency, low noise, and high bandwidth. The secure key rates over transmission distance of 5.005 km with and without consideration of the finite-size effect are 273.25 Mbps and 1.09 Gbps. The use of the PSP method boosts the asymptotic secret key rate of CVQKD to Gbps level for the first time, to our knowledge, within the range of the access network, which provides an effective and secure key distribution strategy for high-speed quantum cryptography access communication.
Passive state preparation (PSP) continuous variable quantum key distribution (CVQKD) drops out optical amplitude and phase modulators, making this scheme suitable for application in space-confined situations. In this paper, we propose a satellite-mediated PSP-CVQKD scheme. To improve the performance of the scheme further, we introduce a phase-insensitive amplifier (PIA) at the receiver side. Based on the detailed noise model and channel parameter estimation analysis, we perform numerical simulations of the proposed scheme while the finite-size effect is considered. Simulation results show that the satellite-mediated PSP-CVQKD is feasible in both downlink and uplink cases based on typical system parameters. The performance can be improved at a relatively low satellite altitude when the PIA is used. Our analysis demonstrates that the proposed scheme may be a potentially cost-effective solution for future chip-scale CVQKD over satellite-mediated links.
Abstract Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CVQKD) protocol can allow authenticated users to share secret key with unconditional security. So far, all previous experimental implementations of GMCS CVQKD schemes are based on active modulations, i.e. amplitude and phase modulators and quantum random number generator (QRNG) are required. However, high-speed modulation with high extinction ratio and stability is challenging, which is extremely remarkable in chip-scale silicon photonic realization. While the passive-state-preparation (PSP) CVQKD scheme, which explores the intrinsic field fluctuations of a thermal source, avoids the uses of active modulations and QRNG. In this paper, we experimentally realize the intact PSP CVQKD through a realistic optical fiber channel using off-the-shelf amplified spontaneous emission source. In particular, specially designed frame synchronization method is used to build the correlation between the data measured from the two legitimate parties, and excess noise are synthetically controlled to generate secure secret keys at the metro-area distances when considering the practical and non-negligible finite-size effects under collective Gaussian attacks. Due to the avoidance of modulators and QRNG, the passive state encoding scheme provides a promising direction of applicable high-speed, chip-based and even sunlight-based CVQKD with less cost and complexity.
Continuous-variable quantum key distribution (CVQKD) using passive state preparation (PSP) offers low-cost, high-rate secure communication. However, the existing PSP-CVQKD scheme with a transmitted local oscillator has high photon leakage noise and poor stability, making it unsuitable for high-loss transmission. In this work, for the first time, we propose and implement a local local oscillator (LLO) CVQKD system using a self-referenced (SR) PSP scheme, and give a theoretical proof of the equivalence of the PSP and GMCS protocol using temporal-mode theory. By employing the novel self-referenced pilot scheme to achieve high-precision time-varying frequency and phase compensation algorithms, we significantly improve the system' s signal-to-noise ratio and stability. The system achieves a record-high asymptotic secret key rate of 10.34 Mbps over a free-space channel with up to 23.5 dB loss, while maintaining low excess noise and robust performance under turbulent conditions. This work establishes the feasibility of SR-LLO CVQKD, providing a practical pathway toward secure, high-rate quantum communication in realistic environments.
It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution (CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source. It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.
Continuous-variable quantum key distribution (CV-QKD) provides an effective way to obtain the high secret key rate, but is limited by practical techniques. To overcome this limitation, we investigate the performance of CV-QKD protocols when non-Gaussian operations are applied to both sides of the channels, including photon subtraction and addition, and photon catalysis. A comparison is also made between Gaussian modulation and non-Gaussian modulation. We show that the optimal transmission distance cannot be improved by non-Gaussian modulation at the sender's side, but it can be improved by single-photon catalysis at the receiver's side. For a given modulation variance that exceeds a certain threshold, the performance of the zero-photon catalysis at the sender's side is the best when compared with other non-Gaussian modulations (except single-photon catalysis at the receiver's side), and it can always reach the optimal distance. Our paper will provide a useful insight for the use of non-Gaussian modulation to other CV-QKD protocols.