Achieving metrological precision limits through post-selection

TL;DR

This paper experimentally compares two post-selection protocols in optical measurements, demonstrating how each approaches quantum limits of estimation precision and highlighting their robustness and information sharing mechanisms.

Contribution

It provides an experimental comparison of weak-value amplification and a non-amplifying post-selection method, showing both can reach quantum limits of measurement precision.

Findings

Both protocols approach the quantum Cramér-Rao bound.

Information is obtained from both measurement outcomes and post-selection statistics.

The non-amplifying method is more robust for parameter estimation.

Abstract

Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to experimentally explore two different post-selection protocols for the estimation of a small parameter: a weak-value amplification procedure and an alternative method, that does not provide amplification, but nonetheless is shown to be more robust for the sake of parameter estimation. Each technique leads approximately to the saturation of quantum limits for the estimation precision, expressed by the Cram\'er-Rao bound. For both situations, we show that information on the parameter is obtained jointly from the measuring device and the post-selection statistics.