Energy measurements remain thermometrically optimal beyond weak coupling

TL;DR

This paper develops a perturbative framework for quantum thermometry at finite coupling, showing local energy measurements are optimal for temperature estimation up to second order, regardless of probe or sample specifics.

Contribution

It introduces a second-order perturbative theory for quantum thermometry at finite coupling and demonstrates the optimality of local energy measurements for temperature estimation.

Findings

Local energy measurements achieve thermometric precision to second order.

The quantum Fisher information can be expressed in closed form.

The formalism applies without assumptions on dynamical timescales or probe/sample nature.

Abstract

We develop a general perturbative theory of finite-coupling quantum thermometry up to second order in probe-sample interaction. By assumption, the probe and sample are in thermal equilibrium, so the probe is described by the mean-force Gibbs state. We prove that the ultimate thermometric precision can be achieved - to second order in the coupling - solely by means of local energy measurements on the probe. Hence, seeking to extract temperature information from coherences or devising adaptive schemes confers no practical advantage in this regime. Additionally, we provide a closed-form expression for the quantum Fisher information, which captures the probe's sensitivity to temperature variations. Finally, we benchmark and illustrate the ease of use of our formulas with two simple examples. Our formalism makes no assumptions about separation of dynamical timescales or the nature of either the probe or the sample. Therefore, by providing analytical insight into both the thermal sensitivity and the optimal measurement for achieving it, our results pave the way for quantum thermometry in setups where finite-coupling effects cannot be ignored.