Entanglement Structure Certification Based on Energy-Restricted State Discrimination

The certification of entanglement in multipartite scenarios is crucial for the advancement of quantum technologies, particularly for the realization of large-scale quantum networks. Here, we introduce a method to certify the structure of the entanglement in ensembles of quantum states with limited energy based on a state discrimination game played by multiple distant and uncharacterized parties. The optimal success probability of this game forms a strict hierarchy, determined by the number of bipartitions and the size of the entangled subsets in each state of the underlying ensemble. The game can be optimally won using a single, fixed measurement setting shared by all parties, regardless of the specific entanglement structure. We further demonstrate that both the performance and noise robustness of our method improve in the multipartite regime, scaling exponentially with the number of parties. Consequently, our approach enables the exclusion of entire structural classes, thereby certifying the structure of multipartite entanglement.