  The article introduces efficient quantum state tomography schemes for qutrits
and entangled qubits subject to pure decoherence. We implement the dynamic
state reconstruction method for open systems sent through phase-damping
channels which was proposed in: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the
current article we prove that two distinct observables measured at four
different time instants suffice to reconstruct the initial density matrix of a
qutrit with evolution given by a phase-damping channel. Furthermore, we
generalize the approach in order to determine the optimal criteria for quantum
tomography of entangled qubits. Finally, we prove two universal theorems
concerning the minimal number of distinct observables required for quantum
tomography of qudits. We believe that dynamic state reconstruction schemes
bring significant advancement and novelty to quantum tomography since they
allow to reduce the number of distinct measurements required to solve the
problem, which is important from the experimental point of view.
