  We introduce two forms of correlations on two $d$-level (qudit) systems for
entanglement detection. The correlations can be measured via experimentally
tractable two local measurement settings and their separable bounds are
determined by discrete Fourier-based uncertainty relations. They are useful to
estimate lower bounds of the Schmidt number in order to clarify generation of a
genuine qudit entanglement. We also present inseparable conditions for
multi-qudit systems associated with the qudit stabilizer formalism as another
role of the correlations on the inseparability problem.
