Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

TL;DR

This paper presents a protocol for Heisenberg-limited parameter estimation in linear networks using multi-channel homodyne measurements, without prior information or network adaptation, suitable for experimental implementation.

Contribution

It introduces a non-adaptive, Heisenberg-limited metrology protocol that does not require auxiliary networks or prior parameter knowledge.

Findings

Achieves Heisenberg-scaling sensitivity in linear network parameter estimation.

Utilizes a single-mode squeezed state with homodyne detection across multiple channels.

Eliminates the need for prior coarse estimation or network adaptation.

Abstract

We show a protocol achieving the ultimate Heisenberg-scaling sensitivity in the estimation of a parameter encoded in a generic linear network, without employing any auxiliary networks, and without the need of any prior information on the parameter nor on the network structure. As a result, this protocol does not require a prior coarse estimation of the parameter, nor an adaptation of the network. The scheme we analyse consists of a single-mode squeezed state and homodyne detectors in each of the $M$ output channels of the network encoding the parameter, making it feasible for experimental applications.