Invasiveness of non-equilibrium quantum thermometry

TL;DR

This paper investigates the relationship between information gain and heat absorption in non-equilibrium quantum thermometry, showing that optimal probing minimizes invasiveness and that strong coupling enhances accuracy without excessive heat transfer.

Contribution

It introduces a time-optimal probing scheme for pure-dephasing spin probes, linking measurement accuracy with heat absorption and thermodynamic costs in quantum thermometry.

Findings

Optimal probing time limits heat absorbed per shot.

Strong probe-sample coupling increases accuracy linearly.

Heat absorption saturates at finite value despite increasing coupling.

Abstract

One of the main advantages expected from using quantum probes as thermometers is non invasiveness, i.e., a negligible perturbation to the thermal sample. However, invasiveness is rarely investigated explicitly. Here, focusing on a pure-dephasing spin probe in a bosonic sample, we show that there is a non-trivial relation between the information on the temperature gained by a quantum probe and the heat absorbed by the sample due to the interaction. We show that optimizing over the probing time, i.e. considering a time-optimal probing scheme, also has the benefit of limiting the heat absorbed by the sample in each shot of the experiment. For such time-optimal protocols, we show that it is advantageous to have very strong probe-sample coupling, since in this regime the accuracy increases linearly with the coupling strength, while the amount of heat per shot saturates to a finite value. Since in pure-dephasing models the absorbed heat corresponds to the external work needed to couple and decouple the probe and the sample, our results also represent a first step towards the analysis of the thermodynamic and energetic cost of quantum thermometry.