On the relation between transformation dynamics and quantum statistics in weak measurements

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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.