Free-space quantum cryptography holds significant potential for enabling global quantum communication networks. This paper proposes a free-space continuous-variable quantum secret sharing (CV-QSS) protocol employing a local local oscillator (LLO). The proposed protocol simplifies the system architecture by requiring only two heterodyne detections at the dealer’s side, thereby eliminating the additional noise and complexity associated with coherent measurements at each participant’s side in conventional schemes. Theoretically, we establish a channel transmittance model that comprehensively incorporates the effects of rain extinction and atmospheric turbulence, and derive the bound of the secret key rate. Experimentally, we systematically evaluate the impact of weather conditions and atmospheric turbulence on protocol performance and conduct comparative evaluations against existing schemes. The results demonstrate that the proposed protocol outperforms the previously proposed free-space LLO-based CV-QSS protocol in terms of key rate, transmission distance, noise tolerance, and participant capacity. Furthermore, this protocol supports secret sharing among 5 participants over 75 km or up to 37 participants within 10 km, outperforming the LLO-based CV-QSS system in a fiber channel. This study validates the potential of free-space CV-QSS as a viable solution for medium-to-long-distance and multi-user quantum secret sharing.
Free-space quantum cryptography holds significant potential for enabling global quantum communication networks. This paper proposes a free-space continuous-variable quantum secret sharing (CV-QSS) protocol employing a local local oscillator (LLO). The proposed protocol simplifies the system architecture by requiring only two heterodyne detections at the dealer’s side, thereby eliminating the additional noise and complexity associated with coherent measurements at each participant’s side in conventional schemes. Theoretically, we establish a channel transmittance model that comprehensively incorporates the effects of rain extinction and atmospheric turbulence, and derive the bound of the secret key rate. Experimentally, we systematically evaluate the impact of weather conditions and atmospheric turbulence on protocol performance and conduct comparative evaluations against existing schemes. The results demonstrate that the proposed protocol outperforms the previously proposed free-space LLO-based CV-QSS protocol in terms of key rate, transmission distance, noise tolerance, and participant capacity. Furthermore, this protocol supports secret sharing among 5 participants over 75 km or up to 37 participants within 10 km, outperforming the LLO-based CV-QSS system in a fiber channel. This study validates the potential of free-space CV-QSS as a viable solution for medium-to-long-distance and multi-user quantum secret sharing.
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.
Abstract Although continuous-variable quantum secret sharing (CVQSS) has been theoretically proven to be secure, it may still be vulnerable to various local oscillator (LO) attacks. To close this loophole, here we propose a practical CVQSS scheme using local LO (LLO-CVQSS), where LO is no longer generated by each user but is locally generated by the legitimate dealer. This waives the necessity that all LOs have to be transmitted through untrusted channels, making CVQSS system naturally immune to all LO-aimed attacks and enhancing its practical security. We also develop a dedicated phase compensation method for LLO-CVQSS to control the phase noise, and construct a noise model that derives its security bound against both eavesdroppers and dishonest users. Finally, numerical simulation shows that LLO-CVQSS can support 30 users at the same time and the maximal transmission distance reaches 112 km, revealing its potential for building large-scale practical quantum communication networks.
Although quantum key distribution (QKD) enables information-theoretically secure key distribution, it is mainly designed for point-to-point communication and cannot directly support multi-user collaborative scenarios. To address this limitation, quantum secret sharing (QSS) has been proposed to enable secure multiparty key sharing. However, most existing QSS protocols rely on a single-input single-output (SISO) channel, which limits the achievable secret key rate (SKR) and transmission distance. This paper proposes a continuous-variable (CV) QSS protocol based on a multiple-input multiple-output (MIMO) architecture operating in the terahertz (THz) band. In the proposed scheme, transmit-receive beamforming decomposes the MIMO channel into multiple parallel SISO subchannels, thereby improving both the SKR and transmission distance. We describe the QSS transmission procedure and derive the SKR expressions for eight protocol variants under Gaussian collective attacks. Specifically, Gaussian modulation and passive modulation are considered at the transmitter, while homodyne and heterodyne detection are considered at the receiver. Both asymptotic and composable finite-size SKR formulas are derived to characterize the ideal upper-bound performance and the achievable performance under finite resources, respectively. Simulation results show that, under ideal assumptions including perfect channel state information, perfect phase synchronization, and ideal beamforming, the Gaussian-modulation protocol with a 32 x 32 antenna configuration and the passive-modulation protocol with a 1024 x 1024 antenna configuration achieve transmission distances of 14.99 m and 160 m in the atmospheric channel, respectively. These results provide an idealized theoretical benchmark for evaluating the potential performance gains of MIMO-assisted THz CV-QSS in indoor and short-range outdoor wireless networks.
In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subjected to security threats due to various targeted attacks. To solve this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local intrinsic oscillator, in which the intrinsic oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection by using the local intrinsic oscillator and reference phases; post-processing, which involves parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter (KF) is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar KF and vector KF are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even at lower levels, minimizing interference with quantum signals. These results highlight that the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.
Quantum secret sharing (QSS) faces inherent limitations in scaling to multi-user networks due to excess noise introduced by highly asymmetric beam splitters (HABSs) in chain-structured topologies. To overcome this challenge, we propose an optical frequency comb-based continuous-variable QSS (OFC CV-QSS) scheme that establishes parallel frequency channels between users and the dealer via OFC-generated multi-wavelength carriers. By replacing the chain-structured links with dedicated frequency channels and integrating the Chinese remainder theorem (CRT) with a decentralized architecture, our design eliminates excess noise from all users using HABS while providing mathematical- and physical-layer security. Simulation results demonstrate that the scheme achieves a more than 50% improvement in maximum transmission distance compared to chain-based QSS, with significantly slower performance degradation as users scale to 20. Numerical simulations confirm the feasibility of this theoretical framework for multi-user quantum networks, offering dual-layer confidentiality without compromising key rates.
The advent of quantum computers has significantly challenged the security of traditional cryptographic systems, prompting a surge in research on quantum key distribution (QKD). Among various QKD approaches, continuous-variable QKD (CVQKD) offers superior resilience against background noise. However, the local local oscillator (LLO) CVQKD scheme faces substantial physical limitations in scenarios with high channel attenuation, and the large attenuation CVQKD remains unrealized. Bottleneck challenges include ensuring stable low-noise transmission and accurately estimating parameters under fluctuating channel conditions. We propose a continuous-mode theoretical framework that provides an analytical method for time-varying quantum systems within a free-space channel. This framework can achieve high-fidelity LLO-CVQKD in free space without the need for complex, real-time frequency locking and transmittance calibration equipment. It can also enable free-space QKD under large attenuation and high repetition frequency. Through experimental validation, we first demonstrate high-rate secure quantum key distribution over high-loss free-space channels. Specifically, we achieve asymptotic key rates of 76.366 kbps and 403.896 kbps in 25 dB attenuation free-space channels without turbulence and 21.5 dB average attenuation free-space channels with turbulence, respectively. Additionally, we confirm the feasibility of experiments on mildly turbulent atmospheric channels spanning at least 10.5 km using current equipment. Our scheme provides direct insight into constructing an integrated air-ground quantum communication network.