Certified quantum non-demolition measurement of material systems

TL;DR

This paper introduces a method to certify quantum non-demolition measurements of material systems without direct measurement of the signal, enabling verification of non-classical properties in atomic spin ensembles.

Contribution

It develops a covariance matrix-based approach to demonstrate QND criteria without direct signal measurement, facilitating certified QND measurements in material systems.

Findings

Method allows certification of QND measurements without direct signal measurement

Enables application to atomic spin ensembles using existing techniques

Provides a framework for computing QND figures of merit

Abstract

An extensive debate on quantum non-demolition (QND) measurement, reviewed in Grangier et al. [Nature, {\bf 396}, 537 (1998)], finds that true QND measurements must have both non-classical state-preparation capability and non-classical information-damage tradeoff. Existing figures of merit for these non-classicality criteria require direct measurement of the signal variable and are thus difficult to apply to optically-probed material systems. Here we describe a method to demonstrate both criteria without need for to direct signal measurements. Using a covariance matrix formalism and a general noise model, we compute meter observables for QND measurement triples, which suffice to compute all QND figures of merit. The result will allow certified QND measurement of atomic spin ensembles using existing techniques.