Circular Quantum Secret Sharing Based on SWAP Gates

Most existing quantum secret sharing (QSS) protocols can be classified into two types of transmission structures: tree-type and circular-type. Compared to circular-type protocols, tree-type QSS protocols are more difficult to implement in practice due to photon energy loss over long distances, rendering them unsuitable when parties are widely separated. However, circular-type protocols still face two major challenges: (1) maintaining the energy of transmitted photons across a long chain of intermediate nodes is infeasible, and (2) reliance on relay transmission makes them vulnerable to Trojan horse attacks. To address these issues, we propose two novel circular-type QSS protocols based on SWAP gates. The proposed protocols are immune to Trojan horse attacks and offer a practical solution for relay transmission, enabling the long-distance distribution of shadow keys to each agent.