Witnessing network topologies using quantum nonlocality

The study of quantum nonlocal correlations in networks (QNCNs), beyond the standard Bell theory with a single source, involves simulating large-scale quantum communications. The detectability of QNCNs depends on the input sources and selected measurements, and more essentially on the network structures. In this paper, we prove that same-size acyclic networks with different independence degrees can generate distinct sets of QNCNs in the device-independent scenario. We then distinguish two acyclic networks with different independence degrees by comparing the QNCNs generated from them. Furthermore, we show quantum demonstrations of the aforementioned notions in two-qubit-source networks. We investigate the quantitative influence of different network topologies on the detection of QNCNs in acyclic networks with Werner states as sources. Finally, we study how to maintain high independence degrees in networks formed by connecting two networks. This makes the correlations on the newly formed quantum network more likely to be nonlocal. Our research provides an alternative perspective for the well-known graph classification problem, and establishes an intrinsic connection between the graph theory and the foundation of quantum mechanics.