Quantum-cryptography network via continuous-variable graph states

We propose a quantum-cryptography network based on a continuous-variable graph state along with its corresponding quantum key distribution (QKD) protocol. It allows two arbitrary parties in the graph state to share a secret Gaussian key (any-to-any QKD). A mathematical model is established to determine an arbitrary graph state's properties, including the possibility of QKD and the relevant criteria. The general entangling cloner attack strategy is analyzed in detail employing Shannon information theory. Results show that the proposed network is secure against such attack if the graph state meets certain criteria.