Bayesian estimation for collisional thermometry

TL;DR

This paper develops a Bayesian framework for collisional quantum thermometry, providing an experimentally feasible method that optimally estimates temperature and saturates the Cramer-Rao bound over time.

Contribution

It introduces a complete, practical Bayesian approach for collisional thermometry that guarantees optimal estimation and discusses the impact of prior information on measurement accuracy.

Findings

Framework guarantees saturation of the Cramer-Rao bound in the long-time limit

Approach is experimentally friendly and easily implementable

Analyzes the role of prior information using a modified Bayesian bound

Abstract

Quantum thermometry exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation. This highlights the need for constructing concrete estimation strategies. Of particular importance is collisional thermometry, where a series of ancillas are sent sequentially to probe the system's temperature. In this paper we put forth a complete framework for analyzing collisional thermometry using Bayesian inference. The approach is easily implementable and experimentally friendly. Moreover, it is guaranteed to always saturate the Cramer-Rao bound in the long-time limit. Subtleties concerning the prior information about the system's temperature are also discussed, and analyzed in terms of a modified Cramer-Rao bound associated to Van Trees and Sch\"utzenberger.