(n, m, p)-type quantum network configuration and its nonlocality

A quantum network that shares entangled sources among distant nodes enables us to distribute entanglement along the network by suitable measurements. Network nonlocality means that it does not admit a network model involving local variables emitted from independent sources. In this work, we construct an (n, m, p)-type quantum network configuration and then derive the corresponding n-local correlation inequalities based on the assumption of independent sources. As a more general quantum network configuration, it can cover most of the existing network models, such as the typical chain network, star network and ring network, and provides both centerless and asymmetric network topologies, involving cyclic and acyclic configurations. We demonstrate the non-n-locality of the present network by calculating the violation of the n-local inequality with bipartite entangled sources and Pauli measurements. This allows us to simplify the analysis of various network configurations using a general network parameterized by n, m and p.