Multiuser quantum key distribution using quotient graph states derived from continuous-variable dual-rail cluster states

Multipartite entangled states are essential for multiuser quantum cryptography. While large-scale continuous-variable (CV) cluster states, particularly the dual-rail cluster state, have been well studied in measurement-based quantum computation, their cryptographic potential remains underexplored. Here, we propose a three-user conference key protocol using a CV dual-rail cluster state. By applying a node-coloring scheme to the infinite dual-rail graph, we create a six-mode pure graph state ideal for cryptographic tasks. Our results demonstrate near-GHZ (Greenberger-Horne-Zeilinger) performance for quantum conference key agreement (QCKA). Crucially, our protocol uniquely enables bipartite keys post-QCKA, which GHZ states cannot provide. It also surpasses two-mode squeezed vacuum states in generating bipartite keys within downstream-access networks. Considering finite-size effects and impure squeezed states, our scheme remains robust despite experimental imperfections. We also introduce an enhanced method to more accurately estimate bipartite key generation capacity in quantum networks, paving the way for practical multiuser quantum cryptography.