Quantum Thermometry

TL;DR

This paper explores how quantum estimation theory can optimize temperature measurement precision in quantum systems, highlighting the roles of quantum coherence, entanglement, and measurement strategies in enhancing thermometry accuracy.

Contribution

It extends quantum estimation theory to non-Hamiltonian quantities like temperature, analyzing the impact of quantum resources and measurement techniques on thermometry.

Findings

Global measurements relate temperature precision to heat capacity.

Local probing limits accuracy to a mesoscopic heat capacity.

Quantum coherence and entanglement improve measurement speed and accuracy.

Abstract

We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, so that these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.