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Journal of Modern Optics

Improving passive state preparation continuous-variable quantum key distribution with a hybrid linear amplifier

Yaqin Wang, Nana Yu, Wei Zhang, Mengmeng Zhao, Xiting Wang, Sixing Xi

Published Dec 1, 2025• 0 citations
Publisher

Abstract

In this paper, we introduce a hybrid linear amplifier (HLA) at the interface of the passive state preparation (PSP) continuous-variable quantum key distribution (CVQKD) system to increase the protocol’s transmission performance. Specifically, we find that the noiseless linear amplifier (NLA) component of the HLA increases the maximum transmission distance of the PSP protocol, and the deterministic linear amplifier (DLA) increases the secret key rate within ten kilometres. By appropriately tuning the amplifier parameters, the key rate can be optimized for a given transmission distance. Even with a key length of 1010 and excess noise of 0.1 dB, the protocol achieves secure transmission distances of up to 64 km and 20 km in respective scenarios, which are sufficient to meet the requirements of practical quantum communication systems. Our research provides a new technical way to improve the PSP protocol.

DOI
10.1080/09500340.2025.2592132

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In this paper, we introduce a hybrid linear amplifier (HLA) at the interface of the passive state preparation (PSP) continuous-variable quantum key distribution (CVQKD) system to increase the protocol’s transmission performance. Specifically, we find that the noiseless linear amplifier (NLA) component of the HLA increases the maximum transmission distance of the PSP protocol, and the deterministic linear amplifier (DLA) increases the secret key rate within ten kilometres. By appropriately tuning the amplifier parameters, the key rate can be optimized for a given transmission distance. Even with a key length of 1010 and excess noise of 0.1 dB, the protocol achieves secure transmission distances of up to 64 km and 20 km in respective scenarios, which are sufficient to meet the requirements of practical quantum communication systems. Our research provides a new technical way to improve the PSP protocol.
Abstract We propose a method to improve transmission distance of continuous-variable quantum key distribution via a heralded hybrid linear amplifier (HLA), involving an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The phase-insensitive amplification of quantum light states may experience a degradation of signal-to-noise ratio (SNR) of 3dB which can be surmounted by the probabilistic amplification process. The new hybrid amplifier allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. Our equipment could clone unknown coherent states with fidelity surpassing the no-cloning limit by abandoning determinism and using probabilistic methods. The setup has a better compatibility with continuous variable protocols as it only uses Gaussian elements and a post-selection algorithm. The hybrid linear amplifier enhances the SNR and hence the transmission distance of the CVQKD protocol is extended. Both the asymptotic secret key rate and the secret key rate in a finite-size scenario are analyzed in this paper.
In practical quantum communication networks, the scheme of continuous-variable quantum key distribution (CVQKD) faces a challenge that the entangled source is controlled by a malicious eavesdropper, and although it still can generate a positive key rate and security, its performance needs to be improved, especially in secret key rate and maximum transmission distance. In this paper, we proposed a method based on the four-state discrete modulation and a heralded hybrid linear amplifier to enhance the performance of CVQKD where the entangled source originates from malicious eavesdropper. The four-state CVQKD encodes information by nonorthogonal coherent states in phase space. It has better transmission distance than Gaussian modulation counterpart, especially at low signal-to-noise ratio (SNR). Moreover, the hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can improve the probability of amplification success and reduce the noise penalty caused by the measurement. Furthermore, the hybrid linear amplifier can raise the SNR of CVQKD and tune between two types of performance for high-gain mode and high noise-reduction mode, therefore it can extend the maximal transmission distance while the entangled source is untrusted.
We propose a protocol to improve the transmission distance and secure key rate of quantum channels, the NLA-HLA QKD. The untrusted entanglement is sent to users by a quantum channel. It is capable of long transmission distances while maintaining high secure key rates and resisting the higher noise. Using the method of calculating secure key rate with the coherent state, the secure key of the NLA-HLA QKD protocol is derived. The effects of the parameters G and g on the key rate are analyzed through simulation experiments. By regulating the values of G and g, the application range of the protocol can be improved. Optimal parameters are used under specific circumstances to ensure the validity of the protocol.
Continuous-variable quantum secret sharing (CVQSS) enables multiple players (at least three) to share a secret key using weak coherent states, which are easy to prepare and resilient to losses. Despite these advantages, CVQSS encounters challenges such as low secret key rates and limited maximum transmission distances, particularly when dealing with a large number of players. This paper proposes a novel scheme to enhance CVQSS performance by incorporating a heralded hybrid linear amplifier (HHLA). The HHLA combines a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), effectively functioning as an improved noiseless linear amplifier with a higher probability of successful amplification. Additionally, the HHLA offers tunable gain settings, including a high-gain mode and a high noise-reduction mode, to optimize noise penalties form measurements and enhance CVQSS performance. Numerical simulations demonstrate that even with 100 connected nodes, the HHLA-based CVQSS scheme achieves a maximum transmission distance exceeding 60 km.
Developing quantum key distribution (QKD) protocols resistant to losses and noises is of great importance in practice. We show that the maximum transmission distance and tolerable excess noise of the Gaussian modulation (GM) and discrete modulation (DM) CVQKD protocols can be dramatically increased by using a noiseless linear amplifier (NLA). It is proved that a NLA with gain g can increase the maximum transmission distance by 20 /αlog10g km, where a = 0.2 dB/km is the loss coefficient of the fiber channel.
A modified four-state CVQKD protocol is proposed to increase the maximum transmission distance and tolerable excess noise in the presence of Gaussian lossy and noisy channel by using a noiseless linear amplifier (NLA). An ideal NLA with gain ggg can increase the maximum admission losses by 20log10g20{\mathrm{log}}_{10}g20log10​g dB. Further, the imperfections in a practical NLA, such as the finite detection efficiency and imperfect single-photon source, are included in consideration.