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

TL;DR

This paper explores how the imaginary parts of weak values relate to transformation dynamics in quantum systems, linking quantum statistics to the effects of unitary transformations through complex conditional probabilities.

Contribution

It introduces a framework connecting weak measurement outcomes with the dynamical evolution of quantum states via complex probabilities.

Findings

Imaginary parts of weak values reflect transformation dynamics.

Complex conditional probabilities describe quantum state evolution.

Quantum state overlap relates to the dynamical action of unitaries.

Abstract

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.