Verifying Hierarchic Multipartite and Network Nonlocalities with a Unified Method

The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. A unified approach is proposed that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no-signaling correlations. A straightforward method is offered to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. The lifting method is finally applied to verify the correlations derived from quantum networks.