  The ability of fully reconstructing quantum maps is a fundamental task of
quantum information, in particular when coupling with the environment and
experimental imperfections of devices are taken into account. In this context
we carry out a quantum process tomography (QPT) approach for a set of non
trace-preserving maps. We introduce an operator $\OO$ to characterize the state
dependent probability of success for the process under investigation. We also
evaluate the result of approximating the process with a trace-preserving one.
