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Operational approach to open dynamics in the presence of initial correlations

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Quantum process tomography is the experimental procedure
to determine the action of general transformations on quantum states. When an
external environment is interacting with the system these transformations are
called open. We show that if the state of the system and the environment is
correlated, at the beginning of the experiment, then the standard quantum
process tomography procedure fails. It produces results that are nonlinear and
non-positive (i.e., the dynamical map is not completely positive) . These
undesirable behaviours are functions of the preparation procedure employed to
initialise the system. We offer a full resolution to these
difficulties by operationally deriving a procedure for process tomography.

Surprisingly, there are additional benefits that come
along with this procedure, namely quantifying the kickbacks due to the initial