  The quantum speed limit is a fundamental upper bound on the speed of quantum
evolution. However, the actual mathematical expression of this fundamental
limit depends on the choice of a measure of distinguishability of quantum
states. We show that quantum speed limits are universally characterized by the
Schatten-$p$-norm of the generator of quantum dynamics. Since computing
Schatten-$p$-norms can be mathematically involved, we then develop an
alternative approach in Wigner phase space. We find that the quantum speed
limit in Wigner space is fully equivalent to expressions in density operator
space, but that the new bound is significantly easier to compute. Our results
are illustrated for the parametric harmonic oscillator and for quantum Brownian
motion.
