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

TL;DR

The paper addresses the limitation of the linear rate-distance bound in quantum secret sharing (QSS) by proposing a polarization-phase dual-DOF QSS protocol using weak coherent pulses, combining single-photon interference, two-photon interference, and non-interference. It analyzes security under internal attacks and beam-splitting attacks, deriving a key-rate bound and demonstrating resistance to eavesdropping via a detailed security framework. Numerical simulations show the dual-DOF QSS surpasses the linear bound, offers stronger beam-splitting resilience than WCP-Ph-QSS and DPS-TF-QSS, and achieves longer maximum distances with high mean photon numbers (optimal around $μ \approx 0.84$) and distances approaching $\sim 458$ km, with peak key rates around $2\times 10^{-6}$ bit/pulse. The work is experimentally feasible with current technology and holds promise for enabling long-distance, high-capacity quantum networks.

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.

Figures (4)

• Figure 1: Schematic diagram of the dual-DOF QSS protocol under the beam splitting attack. The WCPs are generated from the laser sources. The polarization modulator (Pol-M) and phase modulator (PM) are used to realize the polarization and phase encoding, respectively, and the intensity modulator (IM) realizes the intensity modulation. PBS, BS and VBS represent polarization beam splitter, 50:50 beam splitter and variable beam splitter. QM represents quantum memory. $D_{1H}$, $D_{1V}$, $D_{2H}$, $D_{2V}$ are practical photon detectors.
• Figure 2: $I_E$ of our dual-DOF QSS protocol, WCP-Ph-QSS protocol WCP_Ph_QSS, WCP-Pol-QSS protocol qkd5 and DPS-TF-QSS protocol DPS_TF_QSS under the beam splitting attack altered with $\mu$ at $L=100$ km. $I_E$ of the WCP-Pol-QSS protocol equals to that of the MDI-QKD protocol qkd5.
• Figure 3: The key rates of our dual-DOF QSS protocol, WCP-Ph-QSS protocol WCP_Ph_QSS and WCP-Pol-QSS altered with the communication distance under $\mu=0.84$.
• Figure 4: The key rates of our dual-DOF QSS protocol, the WCP-Ph-QSS protocol WCP_Ph_QSS and the WCP-Pol-QSS altered with the communication distance under $\mu=1.5$.