Uninformed Bayesian Quantum Thermometry

TL;DR

This paper investigates Bayesian quantum thermometry without prior temperature knowledge, proposing new estimators that improve accuracy and range, and analyzing their performance against theoretical bounds.

Contribution

It introduces two novel estimators based on relative deviations for uninformed thermometry, enhancing accuracy and temperature range coverage.

Findings

Mean and median estimators diverge at high temperatures.

Proposed estimators match a modified van Trees bound.

Partially thermalized probes extend temperature sensitivity range.

Abstract

We study the Bayesian approach to thermometry with no prior knowledge about the expected temperature scale, through the example of energy measurements on fully or partially thermalized qubit probes. We show that the most common Bayesian estimators, namely the mean and the median, lead to high-temperature divergences when used for uninformed thermometry. To circumvent this and achieve better overall accuracy, we propose two new estimators based on an optimization of relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements the Cram\'er-Rao bound for smaller probe numbers and unrestricted temperature ranges. Furthermore, we show that, using partially thermalized probes, one can increase the range of temperatures to which the thermometer is sensitive at the cost of the local accuracy.