Post-selected weak measurement beyond the weak value

TL;DR

This paper derives closed-form expressions for quantum measurement statistics in pre- and postselected Gaussian beams, revealing how weak pre-selection and post-selection non-orthogonality influence measurement outcomes and enabling signal amplification beyond traditional limits.

Contribution

It provides a new analytical framework for understanding post-selected weak measurements, extending the applicability beyond the Aharonov-Albert-Vaidman limit.

Findings

Derived closed-form measurement statistics expressions

Identified the interplay between pre-selection weakness and post-selection non-orthogonality

Demonstrated measurement extension beyond traditional weak value limits

Abstract

Closed expressions are derived for the quantum measurement statistics of pre-and postselected gaussian particle beams. The weakness of the pre-selection step is shown to compete with the non-orthogonality of post-selection in a transparent way. The approach is shown to be useful in analyzing post-selection-based signal amplification, allowing measurements to be extended far beyond the range of validity of the well-known Aharonov-Albert-Vaidman limit.