Discrete Fourier-based Correlations for Entanglement Detection

Abstract: 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.