  Quantum Speed Limits (QSLs) rule the minimum time for a quantum state to
evolve into a distinguishable state in an arbitrary physical process. These
fundamental results constrain a notion of distance travelled by the quantum
state, known as the Bures angle, in terms of the speed of evolution set by
nonadiabatic energy fluctuations. We theoretically propose how to measure QSLs
in an ultracold quantum gas confined in a time-dependent harmonic trap. In this
highly-dimensional system of continuous variables, quantum tomography is
prohibited. Yet, QSLs can be probed whenever the dynamics is self-similar by
measuring as a function of time the cloud size of the ultracold gas. This makes
possible to determine the Bures angle and energy fluctuations, as we discuss
for various ultracold atomic systems.
