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We derive upper bounds for Hilbert-Schmidt's quantum coherence of generalstates of a $d$-level quantum system, a qudit, in terms of its incoherentuncertainty, with the latter quantified using the linear and von Neumann'sentropies of the corresponding closest incoherent state. Similar bounds areobtained for Wigner-Yanase's coherence. The reported inequalities are alsogiven as coherence-populations trade-off relations. As an application exampleof these inequalities, we derive quantitative wave-particle duality relationsfor multi-slit interferometry. Our framework leads to the identification ofpredictability measures complementary to Hilbert-Schmidt's, Wigner-Yanase's,and $l_{1}$-norm quantum coherences. The quantifiers reported here for the waveand particle aspects of a quanton follow directly from the defining propertiesof the quantum density matrix (i.e., semi-positivity and unit trace),contrasting thus with most related results from the literature.

Quantitative wave-particle duality relations from the density matrix properties