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

Abstract

In this paper, we discuss the minimal number η of observables Q 1 ,…, Q η , where expectation values at some time instants t 1 ,…,t r 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 Q 1 ,…, Q n at some time instants t 1 < t 2 < … <t r , where n < d 2 − 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).