Optimal Quantum Thermometry with Coarse-grained Measurements

TL;DR

This paper investigates the fundamental limits of quantum thermometry when only coarse-grained energy measurements are feasible, demonstrating that accurate temperature estimation remains possible with limited measurement outcomes.

Contribution

It derives the structure of optimal coarse-grained measurements and applies these results to many-body and nonequilibrium quantum thermometry scenarios.

Findings

Optimal coarse-grained measurements can yield accurate temperature estimates.

Fisher-information scaling remains unchanged under coarse-graining for spin lattices.

Upper bounds are established for probe-based thermometry strategies.

Abstract

Precise thermometry for quantum systems is important to the development of new technology, and understanding the ultimate limits to precision presents a fundamental challenge. It is well known that optimal thermometry requires projective measurements of the total energy of the sample. However, this is infeasible in even moderately-sized systems, where realistic energy measurements will necessarily involve some coarse graining. Here, we explore the precision limits for temperature estimation when only coarse-grained measurements are available. Utilizing tools from signal processing, we derive the structure of optimal coarse-grained measurements and find that good temperature estimates can generally be attained even with a small number of outcomes. We apply our results to many-body systems and nonequilibrium thermometry. For the former, we focus on interacting spin lattices, both at and away from criticality, and find that the Fisher-information scaling with system size is unchanged after coarse-graining. For the latter, we consider a probe of given dimension interacting with the sample, followed by a measurement of the probe. We derive an upper bound on arbitrary, nonequilibrium strategies for such probe-based thermometry and illustrate it for thermometry on a Bose-Einstein condensate using an atomic quantum-dot probe.