Demonstrating quantum advantage for network protocols with practical photonic resources

Quantum networks provide a powerful platform for implementing protocols that outperform their classical counterparts in both functionality and security. To realize their full potential, however, it is essential to ensure they are secure, efficient, and experimen-tally viable. Using high-fidelity polarization-encoded 4-qubit GHZ states generated in a compact double-layer Sagnac interferometer, we experimentally implement a privacy-preserving distributed phase estimation protocol, enabling the reconstruction of a global function without revealing the local information of individual network users. Furthermore, we also implement an information-theoretically secure voting protocol that requires no election authorities and extend its functionality to combine privacy and support for multiple candidates and voter pools. Our results showcase versatile quantum protocols that can address key challenges in secure computation, quantum voting, and quantum networks, all within a practical experimental framework.