Global Quantum Thermometry

TL;DR

This paper introduces a global quantum thermometry framework that improves temperature estimation accuracy when prior knowledge is limited, by establishing a new optimal estimation method and precision limit based on a mean logarithmic error.

Contribution

It develops a comprehensive theory of global quantum thermometry, including an optimal post-processing rule and a global precision limit, advancing beyond local estimation methods.

Findings

Global estimator reduces bias in temperature estimates

Mean logarithmic error is the key figure of merit

Global approach outperforms local estimation in limited-data scenarios

Abstract

A paradigm shift in quantum thermometry is proposed. To date, thermometry has relied on local estimation, which is useful to reduce statistical fluctuations once the temperature is very well known. In order to estimate temperatures in cases where few measurement data or no substantial prior knowledge are available, we build instead a theory of global quantum thermometry. Based on scaling arguments, a mean logarithmic error is shown here to be the correct figure of merit for thermometry. Its full minimisation provides an operational and optimal rule to post-process measurements into a temperature reading, and it establishes a global precision limit. We apply these results to the simulated outcomes of measurements on a spin gas, finding that the local approach can lead to biased temperature estimates in cases where the global estimator converges to the true temperature. The global framework thus enables a reliable approach to data analysis in thermometry experiments.