In this paper, we discuss the minimal number of observables, where expectation values at some time instant determine the trajectory of a d-level quantum system (qudit) governed by the Gaussian semigroup. We assume that the macroscopic information about the system in question is given by the mean values of n selfadjoint operators $Q_1,...,Q_n$ at some time instants $t_1<t_2<...<t_r$, where $n<d^2-1$ and $rleq {rm deg} mu(lambda,bBBL)$. Here $mu(lambda,bBBL)$ stands for the minimal polynomial of the generator of the Gaussian flow.