Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models

In the paper we discuss possible applications of the so-called stroboscopic tomography (stroboscopic observability) to selected decoherence models of 2-level quantum systems. The main assumption behind our reasoning claims that the time evolution of the analyzed system is given by a master equation of the form $\dot{\rho }=\mathbb{L}\rho$ and the macroscopic information about the system is provided by the mean values $m_i(t_j)=Tr(Q_i\rho (t_j))$ of certain observables $\{Q_i{\}}_{i=1}^r$ measured at different time instants $\{t_j{\}}_{j=1}^p$. The goal of the stroboscopic tomography is to establish the optimal criteria for observability of a quantum system, i.e. minimal value of $r$ and $p$ as well as the properties of the observables $\{Q_i{\}}_{i=1}^r$.