Fundamental limits in Bayesian thermometry and attainability via adaptive strategies

TL;DR

This paper establishes fundamental quantum limits on temperature measurement precision using probes at thermal equilibrium, demonstrating adaptive strategies can reach these bounds while non-adaptive methods cannot surpass shot-noise scaling.

Contribution

It derives the ultimate Bayesian thermometry precision bounds and introduces an adaptive protocol that saturates these limits, highlighting the advantage over non-adaptive methods.

Findings

Adaptive strategies can achieve Heisenberg-like scaling in thermometry precision.

Non-adaptive protocols are limited to shot-noise scaling regardless of control.

A no-go theorem shows non-adaptive methods cannot surpass linear scaling.

Abstract

We investigate the limits of thermometry using quantum probes at thermal equilibrium within the Bayesian approach. We consider the possibility of engineering interactions between the probes in order to enhance their sensitivity, as well as feedback during the measurement process, i.e., adaptive protocols. On the one hand, we obtain an ultimate bound on thermometry precision in the Bayesian setting, valid for arbitrary interactions and measurement schemes, which lower bounds the error with a quadratic (Heisenberg-like) scaling with the number of probes. We develop a simple adaptive strategy that can saturate this limit. On the other hand, we derive a no-go theorem for non-adaptive protocols that does not allow for better than linear (shot-noise-like) scaling even if one has unlimited control over the probes, namely access to arbitrary many-body interactions.