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Symmetry

Performance Improvement of Continuous-Variable Quantum Secret Sharing via Heralded Hybrid Linear Amplifier

Kunlin Zhou, Yang Yu, Lining Zeng, Shijie Deng, Ying Guo

Published Jul 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.3390/sym18071214

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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.
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.
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 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.
An improved continuous variable quantum key distribution (CVQKD) approach based on a heralded hybrid linear amplifier (HLA) is proposed in this study, which includes an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The CVQKD, which is based on an amplifier, enhances the signal-to-noise ratio and provides for fine control between high gain and strong noise reduction. We focus on the impact of two types of optical amplifiers on system performance: phase sensitive amplifiers (PSA) and phase insensitive amplifiers (PIA). The results indicate that employing amplifiers, local local oscillation-based CVQKD systems can enhance key rates and communication distances. In addition, the PIA-based CVQKD system has a broader application than the PSA-based system.
Quantum communications can be conveniently implemented by two participants, but quantum secret key sharing (QSS) through multi-participant communication seems difficult in practice. In this paper, we propose a multi-participant QSS scheme with the local local oscillator (LLO) in continuous variable (CV) quantum communications. It allows an honest participant called a dealer to share a secret key with the others, making it possible to establish a secret key if and only if all participants gather together. The LLO scheme, which eliminates the need for the local oscillator (LO) to be propagated in insecure channels, can be used to avoid the potential LO attack in the traditional CVQSS scheme. Numerical simulation shows that the performance of the LLO-based CVQSS can be improved in terms of the maximal transmission distance even if it is performed with the partially trusted noise.
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.