Zero-correlation entanglement vs. Schmidt rank

In this paper, we find the minimal number of correlation tests required to certify independence two classical random variables arbitrary finite support. Moreover, completely characterize constraints implied by zero correlations upon an heterogeneous quantum state, and solve conjecture proposed Ohira in 2020. Finally, first ever algorithm for computing (or checking) Schmidt rank any unknown pure state using only zero-correlation tests, finding a sufficient amount certifying separability or full entanglement.