  A central aim of physics is to describe the dynamics of physical systems.
Schrodinger's equation does this for isolated quantum systems. Describing the
time evolution of a quantum system that interacts with its environment, in its
most general form, has proved to be difficult because the dynamics is dependent
on the state of the environment and the correlations with it. For discrete
processes, such as quantum gates or chemical reactions, quantum process
tomography provides the complete description of the dynamics, provided that the
initial states of the system and the environment are independent of each other.
However, many physical systems are correlated with the environment at the
beginning of the experiment. Here, we give a prescription of quantum process
tomography that yields the complete description of the dynamics of the system
even when the initial correlations are present. Surprisingly, our method also
gives quantitative expressions for the initial correlation.
