Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing

TL;DR

This paper explores how non-Hermitian quantum systems near singular points can be used for highly sensitive sensing, analyzing the ultimate precision limits and the impact of nuisance parameters.

Contribution

It introduces a framework combining multiparameter estimation theory with singular-matrix perturbations to analyze sensitivity divergence in non-Hermitian sensors.

Findings

Sensitivity can diverge near singular points under certain conditions

Nuisance parameters can alter the scaling of measurement errors

Provides tools to determine ultimate precision limits in non-Hermitian sensing

Abstract

Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation of parity-time symmetry, or capitalising on the singular behaviour of the dynamics. In this work, we focus on the possibility of achieving unbounded sensitivity when using the system to sense linear perturbations away from a singular point. By combining multiparameter estimation theory of Gaussian quantum systems with the one of singular-matrix perturbations, we introduce the necessary tools to study the ultimate limits on the precision attained by such singularity-tuned sensors. We identify under what conditions and at what rate can the resulting sensitivity indeed diverge, in order to show that nuisance parameters should be generally included in the analysis, as their presence may alter the scaling of the error with the estimated parameter.