  We study fine-grained uncertainty relations for several quantum measurements
in a finite-dimensional Hilbert space. The proposed approach is based on exact
calculation or estimation of the spectral norms of corresponding positive
matrices. Fine-grained uncertainty relations of the state-independent form are
derived for an arbitrary set of mutually unbiased bases. Such relations are
extended with a recent notion of mutually unbiased measurements. The case of
so-called mutually biased bases is considered in a similar manner. We also
discuss a formulation of fine-grained uncertainty relations in the case of
generalized measurements. The general approach is then applied to two
measurements related to state discrimination. The case of three rank-one
projective measurements is further examined in details. In particular, we
consider fine-grained uncertainty relations for mutually unbiased bases in
three-dimensional Hilbert space.
