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

A quantum network shared 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 universal acyclic network configuration, it can cover most of the existing network models, such as the typical chain-network and star-network, and admit both centerless and asymmetric configurations. Then 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.