  The Schmidt number represents the genuine entanglement dimension of a
bipartite quantum state. We derive simple criteria for the Schmidt number of a
density matrix in arbitrary local dimensions. They are based on the trace norm
of correlations obtained from seminal families of quantum measurements,
specifically symmetric informationally complete measurements and mutually
unbiased bases. Our criteria are strictly stronger than both the well-known
fidelity witness criterion and the computable cross-norms or realignment
criterion.
