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In this paper, we discuss the minimal number η of observables Q1,…, Qη, where expectation values at some time instants t1,…,tr determine the trajectory of a d-level quantum system (“qudit”) governed by the Gaussian semigroup [Formula: see text] We assume that the macroscopic information about the system in question is given by the mean values [Formula: see text] of n selfadjoint operators Q1,…, Qn at some time instants t1< t2 < … <tr, where n < d2 − 1 and r ≤ deg μ(λ, 𝕃). Here μ(λ, 𝕃) stands for the minimal polynomial of the generator [Formula: see text] of the Gaussian flow Φ(t).