Frequency-subspace encoding for multiplexed quantum secret sharing

Quantum secret sharing (QSS) is a multi-party quantum communication protocol that can be realized with bipartite entanglement and relative phase encoding. Previous implementations typically encoded the phase in the pump, applying it across the entire source bandwidth, thereby limiting scalability via wavelength multiplexing. In contrast, we present a variant of the standard QSS protocol that leverages frequency correlations to connect multiple users with a single source. The secret owner, who has access to the source, encodes classical information by applying frequency-dependent phase modulation to a broadband polarization-entangled photon pair. Each frequency channel, therefore, provides an independent QSS session among the secret owner and a pair of users. We demonstrate state fidelities of at least 90% for a channel pair of the 200 GHz ITU grid, a configuration that can be extended to more than 40 frequency bins for the same grid spacing. Notably, despite the use of large grid spacing and the experimental limitations, the system achieves full connectivity of a network of 7 users while maintaining a key fraction of 0.4 bits/photon. These results provide a resource-efficient path toward multi-user secret sharing over wavelength-multiplexed networks, eliminating the need for multiple two-photon or multi-photon sources.