  We present two families of quantum speed limits (QSLs) for finite-dimensional
quantum systems undergoing a general physical process. These QSLs were obtained
using Schatten $\alpha$-norms, firstly exploiting the geometric features of the
space of quantum states, and secondly employing the Holder's inequality for
matrix norms. In particular, for the case of single-qubit states, we find that
the geometric QSL is independent of the Schatten norm chosen, thus revealing a
universality behavior of such quantifiers. Furthermore, we provide a comparison
of these quantum speed limits with existing paradigmatic QSLs in literature,
thus showing that the latter results represent particular cases of a general
class of QSLs related to Schatten $\alpha$-norms. Noteworthy, we address
necessary and sufficient conditions for the tightness of the quantum speed
limit that mostly depends on the populations and quantum coherences of the
evolved single-qubit state, and also present a geometric interpretation for
these set of conditions. Finally, we compare the two QSL obtained for the
dynamics of single-qubit states, also presenting an inequality between them
that has a clear geometrical meaning.
