  In a recent letter one of us pointed out how differences in preparation
procedures for quantum experiments can lead to non-trivial differences in the
results of the experiment. The difference arise from the initial correlations
between the system and environment. Therefore, any quantum experiment that is
prone to the influences from the environment must be prepared carefully. In
this paper, we study quantum process tomography in light of this. We suggest
several experimental setups, where preparation of initial state plays a role on
the final outcome of the experiment. We show that by studying the linearity and
the positivity of the resulting maps the experimenter can determine the nature
of the initial correlations between the system and the environment.
