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Large-scale continuous-variable quantum secret sharing with optical frequency comb

Qijun Zhang, Yuehan Xu, Tao Wang, Xiaojuan Liao, Peng Huang, Guihua Zeng

Published Jul 14, 2026• 0 citations
Publisher

Abstract

Abstract Quantum secret sharing (QSS), as a fundamental cryptographic protocol for future quantum networks, continues to face significant challenges, particularly in the generation of multipartite entanglement and the degradation of entanglement fidelity during distribution, both of which severely limit its scalability. These persistent constraints motivate an alternative approach based on continuous-variable (CV) systems. We propose a CVQSS scheme based on an electro-optically modulated optical frequency comb. The scheme employs a single laser to generate multi-wavelength coherent states, enabling the efficient and flexible construction of secret sharing subnetworks. By incorporating a broadcast-based distribution mechanism, the architecture is scalable to 128 players. Experimental verification with 24 players over a 10 km fiber link demonstrates a secret sharing rate of 6.24 per player under asymptotic conditions and 1.27 Mbps per player under finite-size effects, and a 1.05MB image is secretly shared to six players. This work achieves information-theoretically secure QSS both within and across subnetworks, providing a solid technical foundation for the development of scalable and multifunctional quantum networks.

DOI
10.1186/s43074-026-00271-1

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Abstract Quantum secret sharing (QSS), as a fundamental cryptographic protocol for future quantum networks, continues to face significant challenges, particularly in the generation of multipartite entanglement and the degradation of entanglement fidelity during distribution, both of which severely limit its scalability. These persistent constraints motivate an alternative approach based on continuous-variable (CV) systems. We propose a CVQSS scheme based on an electro-optically modulated optical frequency comb. The scheme employs a single laser to generate multi-wavelength coherent states, enabling the efficient and flexible construction of secret sharing subnetworks. By incorporating a broadcast-based distribution mechanism, the architecture is scalable to 128 players. Experimental verification with 24 players over a 10 km fiber link demonstrates a secret sharing rate of 6.24 per player under asymptotic conditions and 1.27 Mbps per player under finite-size effects, and a 1.05MB image is secretly shared to six players. This work achieves information-theoretically secure QSS both within and across subnetworks, providing a solid technical foundation for the development of scalable and multifunctional quantum networks.
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.
Polychromatic resources have transformed classical communication networks by boosting rate and scalability; quantum communication networks are reaching a similar inflection point. Here, we report a polychromatic continuous-variable quantum communication network enabled by optical frequency combs. The multi-mode density matrices constituted by polychromatic quantum networks are studied. We incorporate finite mode isolation into the security analysis to bound Eve’s accessible information and compute the total network secret key rate. It is demonstrated that, compared to other multiplexing techniques, polychromatic quantum networks can theoretically achieve a secret key rate without decreasing with the increase in users. In the experiment, direct-transmission type and round-trip type quantum communication networks were built using optical frequency combs and dual-comb interference detection technology. The Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) protocol has been validated, with a network capacity of 19 and a total secret key rate of 8.75 Gbps at a uniform distance of 5 km (asymptotic case), 0.82 Mbps at 120 km (finite-size effect), 89.10 Mbps at 40 km (composable security), 13.66 Mbps at 40 km (composable finite-size security). This implementation not only provides technical support for a high-speed multi-node quantum network, but also provides a solution for the future quantum Internet with continuous variables.
In classical communication, the introduction of polychromatic resources has rapidly boosted classical networks' rate and scale. Quantum communication is now at a similar critical stage in its development, and therefore, it is essential to investigate polychromatic quantum communication networks. In this letter, we report a polychromatic continuous-variable quantum communication network enabled by optical frequency combs. The multi-mode density matrices constituted by polychromatic quantum networks are studied. Considering the limited mode isolation, the maximum amount of information that eavesdroppers can obtain is recalculated, therefore, the total secret key rate is provided. We have also demonstrated that, compared to other multiplexing techniques, polychromatic quantum networks can theoretically achieve a secret key rate without decreasing with the increase in users. In the experiment, direct-transmission type and round-trip type quantum communication networks were built using optical frequency combs and dual-comb interference detection technology. The Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) protocol has been validated, with a network capacity of 19 and a total secret key rate of 8.75 Gbps at a uniform distance of 5 km (asymptotic case), 0.82 Mbps at 120 km (finite-size effect), 89.10 Mbps at 40 km (compsable security), 13.66 Mbps at 40 km (compsable finite-size security). This implementation not only provides technical support for a high-speed multi-node quantum network, but also provides a solution for the future quantum Internet with continuous variables.
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.
Secret sharing allows a trusted party (the dealer) to distribute a secret to a group of players, who can only access the secret cooperatively. Quantum secret sharing (QSS) protocols could provide unconditional security based on fundamental laws in physics. While the general security proof has been established recently in an entanglement-based QSS protocol, the tolerable channel loss is unfortunately rather small. Here we propose a continuous variable QSS protocol using conventional laser sources and homodyne detectors. In this protocol, a Gaussian-modulated coherent state (GMCS) prepared by one player passes through the secure stations of the other players sequentially, and each of the other players injects a locally prepared, independent GMCS into the circulating optical mode. Finally, the dealer measures both the amplitude and the phase quadratures of the receiving optical mode using double homodyne detectors. Collectively, the players can use their encoded random numbers to estimate the measurement results of the dealer and further generate a shared key. We prove the unconditional security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss, and discuss various practical issues.
Continuous-variable quantum key distribution (CVQKD) offers high key rates and compatibility with classical optical communications. Developing scalable and efficient CVQKD networks will facilitate the deployment of large-scale quantum communication networks. This paper proposes a CVQKD network based on the untrusted entanglement states of an optical frequency comb. The scheme generates Einstein-Podolsky-Rosen states with a frequency comb structure via a type-II optical parametric oscillator. By employing the entanglement-in-the-middle scheme, a source-untrusted fully connected CVQKD network capable of distributing secret keys simultaneously can be formed. We analyze the security of the system in the asymptotic and finite-size cases. Simulation results show that with careful control of system loss and noise, the proposed scheme is feasible for deploying a short-distance fully connected CVQKD network. Loss will be the main factor limiting system performance. The proposed scheme offers a new perspective for a multi-user fully connected CVQKD network.