Simultaneous Verification of Genuine Multipartite Nonlocality and Full Network Nonlocality

Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been investigated separately. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources enables the certification of the nonclassicality of all sources. In this Letter, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations that cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high-fidelity photonic quantum network by violating a single network Bell inequality.