Efficient Estimation of Multiple Temperatures via a Collisional Model

TL;DR

This paper introduces a quantum thermometric protocol within the collisional model to accurately estimate multiple temperatures, utilizing controlled rotations and ancillary correlations to enhance precision beyond traditional limits.

Contribution

It develops a systematic multiparameter quantum metrology strategy for temperature estimation, including conditions for Fisher information matrix invertibility and methods to improve estimation accuracy.

Findings

Controlled rotations eliminate parameter interdependencies.

Ancillary correlations further enhance Fisher information.

Ancillary system size influences estimation efficiency.

Abstract

We present a quantum thermometric protocol for the estimation of multiple temperatures within the collisional model framework. Employing the formalism of multiparameter quantum metrology, we develop a systematic strategy to estimate the temperatures of several thermal reservoirs with minimal estimation error. We prove a necessary and sufficient condition for the singularity of the Fisher information matrix for a bi-parametrized qubit state. By using controlled rotations of ancillary systems between successive interaction stages, we eliminate parameter interdependencies, thereby rendering the quantum Fisher information matrix non-singular. Remarkably, we demonstrate that precision enhancement in the joint estimation of multiple temperatures can be achieved even in the absence of correlations among the ancillas, surpassing the corresponding thermal Fisher information limits. Exploiting correlations within the ancillary system yields additional enhancement of Fisher information. Finally, we identify the dimensionality of the ancillary systems as a key factor governing the efficiency of multiparameter temperature estimation.