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