Complete characterization of post-selected quantum statistics using weak measurement tomography

TL;DR

This paper demonstrates that quantum state reconstruction via weak measurements allows for a complete statistical description of post-selected quantum systems, linking measurement outcomes to pre-measurement properties.

Contribution

It introduces a method to characterize post-selected quantum statistics through weak measurement tomography, providing a new understanding of quantum state collapse.

Findings

Weak measurements enable state reconstruction with negligible back-action.

Post-selection corresponds to a statistical decomposition of the initial state.

Quantum collapse can be interpreted as classical probability update.

Abstract

The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is also valid for the post-selected sub-ensembles usually considered in weak measurement paradoxes. It is shown that post-selection can then be identified with a statistical decomposition of the initial density matrix into transient density matrices conditioned by the anticipated measurement outcomes. This result indicates that it is possible to ascribe the properties determined by the final measurement outcome to each individual quantum system before the measurement has taken place. The ``collapse'' of the pure state wavefunction in a measurement can then be understood in terms of the classical ``collapse'' of a probability distribution as new information becomes available.