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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 $$\Phi (t)\rho = {1 \over {\sqrt {2\pi t} }}\int\limits_{ - \infty }^\infty dse^{ - s^2 /(2t)_e - iHs_{\rho e} iHs}$$. We assume that the macroscopic information about the system in question is given by the mean values Ej(Qi) = tr(Qiρ(tj)) of n selfadjoint operators Q1, …, Qn at some time instants t1 t2 tr, where n d2− 1 and r⩽ deg μ(λ, $${\Bbb L}$$). Here μ(λ, $${\Bbb L}$$) stands for the minimal polynomial of the generator $${\Bbb L}\rho = - \frac{1}{2}\left[ {H,\left[ {H,\rho } \right]} \right]$$ of the Gaussian flow Φ(t).

On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups