Near-Deterministic Weak-Value Metrology via Collective non-Linearity

TL;DR

This paper introduces a quantum metrology scheme using collective non-linear interactions that significantly improves success probability and weak value amplification, enabling near-deterministic measurements of small parameters.

Contribution

It presents a novel collective non-linear approach that achieves super-extensive success probability growth alongside extensive weak value amplification.

Findings

Success probability grows super-extensively with system size.

Weak value amplification becomes extensive, enhancing measurement sensitivity.

Proposed experimental implementation demonstrates practical feasibility.

Abstract

Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.