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arXiv:2601.06919 · Applied Physics Letters

High capacity dual degrees of freedom quantum secret sharing protocol beyond the linear rate-distance bound

Meng-Dong Zhu, Cheng Zhang, Shi-Pu Gu, Xing-Fu Wang, Ming-Ming Du, Wei Zhong, Lan Zhou, Yu-Bo Sheng

quant-phSubmitted Jan 11, 2026• Announced Jan 13, 2026• 0 citations
v1 · Jan 11, 2026v2 · Jan 15, 2026
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Abstract

Quantum secret sharing (QSS) is the multipartite cryptographic primitive. Most of existing QSS protocols are limited by the linear rate-distance bound, and cannot realize the long-distance and high-capacity multipartite key distribution. This paper proposes a polarization (Pol) and phase (Ph) dual degrees of freedom (dual-DOF) QSS protocol based on the weak coherent pulse (WCP) sources. Our protocol combines the single-photon interference, two-photon interference and non-interference principles, and can resist the internal attack from the dishonest player. We develop simulation method to estimate its performance under the beam splitting attack. The simulation results show that our protocol can surpass the linear bound. Comparing with the differential-phase-shift twin-field QSS and WCP-Ph-QSS protocols, our protocol has stronger resistance against the beam splitting attack, and thus has longer maximal communication distance and higher key rate. By using the WCPs with high average photon number ($μ$ = 1.5), our protocol achieves a key rate about 5.4 times of that in WCP-Ph-QSS protocol. Its maximal communication distance (441.7 km) is about 7.9% longer than that of the WCP-Ph-QSS. Our protocol is highly feasible with current experimental technology and offers a promising approach for long-distance and high-capacity quantum networks.

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Quantum secret sharing (QSS) is the multipartite cryptographic primitive. Most of existing QSS protocols are limited by the linear rate-distance bound, and cannot realize the long-distance and high-capacity multipartite key distribution. This paper proposes a polarization (Pol) and phase (Ph) dual degrees of freedom (dual-DOF) QSS protocol based on the weak coherent pulse (WCP) sources. Our protocol combines the single-photon interference, two-photon interference and non-interference principles, and can resist the internal attack from the dishonest player. We develop simulation method to estimate its performance under the beam splitting attack. The simulation results show that our protocol can surpass the linear bound. Comparing with the differential-phase-shift twin-field QSS and WCP-Ph-QSS protocols, our protocol has stronger resistance against the beam splitting attack, and thus has longer maximal communication distance and higher key rate. By using the WCPs with high average photon number (μμμ = 1.5), our protocol achieves a key rate about 5.4 times of that in WCP-Ph-QSS protocol. Its maximal communication distance (441.7 km) is about 7.9% longer than that of the WCP-Ph-QSS. Our protocol is highly feasible with current experimental technology and offers a promising approach for long-distance and high-capacity quantum networks.
Quantum secret sharing (QSS) is essential for multiparty quantum communication, which is one of cornerstones in the future quantum internet. However, a linear rate-distance limitation severely constrains the secure key rate and transmission distance of QSS. Here, we present a practical QSS protocol among three participants based on the differential phase shift scheme and twin field ideas for the solution of high-efficiency multiparty communication task. In contrast to a formerly proposed differential phase shift QSS protocol, our protocol can break the linear rate-distance bound, theoretically improving the secret key rate by three orders of magnitude in a 300-km-long fiber. Furthermore, the new protocol is secure against Trojan horse attacks that cannot be resisted by previous differential phase shift QSS.
Twin-field quantum key distribution (TFQKD) enables two distant parties to establish a shared secret key, by interfering weak coherent pulses (WCPs) in an intermediate measuring station. This allows TFQKD to reach greater distances than traditional QKD schemes and makes it the only scheme capable of beating the repeaterless bound on the bipartite private capacity. Here, we generalize TFQKD to the multipartite scenario. Specifically, we propose a practical conference key agreement protocol that only uses WCPs and linear optics and prove its security with a multiparty decoy-state method. Our protocol allows an arbitrary number of parties to establish a secret conference key by single-photon interference, enabling it to overcome recent bounds on the rate at which conference keys can be established in quantum networks without a repeater.
Quantum secret sharing (QSS) is a typical multipartite cryptographic primitive, which is an important part of quantum communication network. Existing QSS protocols generally require basis matching, which would waste the precious quantum resource and increase the classical communication round. Moreover, the basis selection makes QSS face weak random security vulnerabilities. We propose an efficient QSS protocol without the basis matching. In the protocol, the dealer and partners share a polarization-momentum hyperentangled Greenberger-Horne-Zeilinger (GHZ) state and encode keys in the polarization degree of freedom (DOF). The dealer decodes the transmitted keys relying on the nonlocal hyperentanglement-assisted polarization GHZ state analysis. Our QSS protocol is unconditionally secure in theory. We develop simulation method to estimate its performance in practical environment. Our protocol has three advantages. First, it does not require the basis matching and can completely distinguish eight encoded polarization GHZ states, which increases the utilization rate of entanglement resources to 100 % and increases the key generation rate by an order of magnitude. Second, it only requires one round of classical communication, and thus reduces the key generation time by 69.4 % . Third, it can eliminate the weak random security vulnerabilities associated with the basis selection and enhance QSS’s practical security. Meanwhile, our protocol only uses linear optical elements, which makes it practically feasible. Our QSS protocol has application potential in the future quantum communication network.
Quantum secret sharing (QSS) is a typical multipartite cryptographic primitive, which is an important part of quantum communication network. Existing QSS protocols generally require basis selection and matching, which would increase the quantum resource consumption and classical communication round, and also face weak random security vulnerabilities. We propose an efficient hyperentanglement-based QSS protocol without the basis selection, in which the dealer and partners share a polarization-momentum hyperentangled Greenberger-Horne-Zeilinger (GHZ) state and encode keys in the polarization degree of freedom (DOF). The dealer decodes the transmitted keys relying on the nonlocal hyperentanglement-assisted polarization GHZ state analysis. Our QSS protocol is unconditionally secure in theory. We develop simulation method to estimate its performance in practical environment. Compared with the QSS based on the GHZ state, our protocol has several advantages. First, it does not require basis selection and can completely distinguish eight polarization GHZ states, which can improve the utilization rate of entanglement resources to 100%\%% and increase the key generation rate by an order of magnitude. Second, it only requires one round of classical communication, and thus can reduce key generation time by 69.4%\%%. Third, it can eliminate the weak random security vulnerabilities associated with the basis selection. Finally, our protocol only uses linear optical elements, which makes it practically feasible. Our QSS protocol has potential application in future quantum communication network.
Quantum secret sharing (QSS) plays a critical role in building the distributed quantum networks. Device-independent (DI) QSS provides the highest security level for QSS. However, the photon transmission loss and extremely low multipartite entanglement generation rate largely limit DI QSS's secure photon transmission distance (less than 1 km) and practical key generation efficiency. To address the above-mentioned drawbacks, we propose the quantum memory-assisted (QMA) DI QSS protocol based on single-photon sources (SPSs). The single photons from the SPSs are used to construct long-distance multipartite entanglement channels with the help of the heralded architecture. The heralded architecture enables our protocol to have an infinite secure photon transmission distance in theory. The QMA technology can not only increase the multi-photon synchronization efficiency but also optimize the photon transmittance to maximize the construction efficiency of the multipartite entanglement channels. Our protocol achieves the practical key generation efficiency seven orders of magnitude higher than that of the existing DI QSS protocols based on cascaded spontaneous parametric downconversion sources and six orders of magnitude higher than that of the DI QSS based on SPSs without QMA. Our protocol has modular characteristics and is feasible under the current experimental technical conditions. Combining with the advanced random key generation basis strategy, the requirement on experimental devices can be effectively reduced. Our protocol is expected to promote the development of long-distance and high-efficiency DI quantum network in the future.
Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit in the point-to-point QKD without a quantum repeater and achieve high key rates over long distances. However, TF-QKD protocol and its variants commonly use weak coherent pulses (WCPs) as light sources. The vacuum part of WCP accounts for a large proportion, resulting in the lower photon detection rate of the communication receiver, which leads to a shorter transmission distance of the secret key. In this paper, we propose an active-decoy TF-QKD protocol with heralded single-photon source (HSPS), which can achieve higher key rate and longer transmission distance than the active-decoy TF-QKD protocol with WCPs. Also, in order to resist the side channel attacks caused by actively modulating intensity of the pulses, we propose a passive-decoy TF-QKD protocol with HSPS to enhance the security, which can perform almost as good as the active-decoy TF-QKD protocol with WCPs.