Incompletely characterized processes can be used for state tomography. We formalize this idea and show how to chose processes that ensure invertibility for the unknown state, as well as the unknown process parameters.
We extend the idea of using a incompletely characterized process to do quantum state tomography by including the possibility that the process itself is not unitary. We study a to level atom whose dipole moment is unknown and that undergoes spontaneous emission and is irradiated by a laser whose phase and intensity can be controlled at will. We show that by using five different parameter settings of the electric field of the laser it is possible two reconstruct the state, and obtain the unknown spontaneous emission rate and dipole moment of the atom.