Fig. 4: Sample complexities for verifying the Bell state and GHZ states in three different scenarios.

In standard QSV, the Bell state and GHZ states can be verified with the same sample complexity42,57. In the SDI scenario, the isotropic protocol is chosen for verifying the Bell state and the optimized equator + Z protocol is chosen for verifying the GHZ states. In the DI scenario, the Mermin inequality is employed for verifying the three-qubit GHZ state46,50. Here the significance level is chosen to be δ = 0.01.