  Experimentally, the imaginary parts of complex weak values are obtained from
the response of the system to small unitary phase shifts generated by the
target observable. The complex conditional probabilities obtained from weak
measurements can therefore be explained in terms of transformation dynamics.
Specifically, the complex phase of weak conditional probabilities provides a
complete description of the transformation dynamics between the initial and the
final state generated by the intermediate states. The result is a measure of
quantum state overlap that relates quantum statistical properties directly to
the dynamical action of unitary transformations.
