  The uncertainty principle is one of the fundamental features of quantum
mechanics and plays a vital role in quantum information processing. We study
uncertainty relations based on metric-adjusted skew information for finite
quantum observables. Motivated by the paper [Physical Review A 104, 052414
(2021)], we establish tighter uncertainty relations in terms of different norm
inequalities. Naturally, we generalize the method to uncertainty relations of
metric-adjusted skew information for quantum channels and unitary operators. As
both the Wigner-Yanase-Dyson skew information and the quantum Fisher
information are the special cases of the metric-adjusted skew information
corresponding to different Morozova-Chentsov functions, our results generalize
some existing uncertainty relations. Detailed examples are given to illustrate
the advantages of our methods.
