  Given the state of a quantum system, one can calculate the expectation value
of any observable of the system. However, the inverse problem of determining
the state by performing different measurements is not a trivial task. In
various experimental setups it is reasonably straightforward to reconstruct the
state of a quantum system employing linear tomographic technique. In this way
the elements of the density matrix can be linearly related to a set of measured
quantities. But since different observables of a quantum system are not
commuting with each other, one often has to perform series of successive
measurements of observables which cannot be done simultaneously. Simultaneous
measurement of observables cost less time and energy and is more beneficial. In
this paper we review the strategy of quantum state tomography with simultaneous
measurement of commuting observables. This can be done by introducing an
assistant system of which the state is known. We show that the interaction
between the assistant and the system of interest within different frame works
allows the reconstruction of the state of the system. Specifically, we consider
a two-level system and reconstruct its initial state by introducing an
assistant which can be either another two-level system or a single cavity mode
of the electromagnetic field.
