  Temporal correlations in quantum mechanics are the origin of several
non-classical phenomena, but they depend on the dimension of the underlying
quantum system. This allows one to use such correlations for the certification
of a minimal Hilbert space dimension. Here we provide a theoretical proposal
and an experimental implementation of a device-independent dimension test,
using temporal correlations observed on a single trapped $^{171}$Yb$^+$ ion.
Our test goes beyond the prepare-and-measure scheme of previous approaches,
demonstrating the advantage of genuine temporal correlations.
