Characterization of classical Gaussian processes using quantum probes

TL;DR

This paper explores how a single qubit can be used as a quantum probe to effectively characterize classical Gaussian noise, optimizing measurement strategies through quantum estimation theory.

Contribution

It introduces a method to optimize probe state, interaction time, and measurement for noise characterization using quantum estimation theory.

Findings

Optimal measurement settings identified for noise parameter estimation

Maximum likelihood estimator approaches unbiasedness after few thousand measurements

Simulation results demonstrate effective noise characterization with minimal measurements

Abstract

We address the use of a single qubit as a quantum probe to characterize the properties of classical noise. In particular, we focus on the characterization of classical noise arising from the interaction with a stochastic field described by Gaussian processes. The tools of quantum estimation theory allow us to find the optimal state preparation for the probe, the optimal interaction time with the external noise, and the optimal measurement to effectively extract information on the noise parameter. We also perform a set of simulated experiments to assess the performances of maximum likelihood estimator, showing that the asymptotic regime, where the estimator is unbiased and efficient, is approximately achieved after few thousands repeated measurements on the probe system.