Cost-effective temperature estimation strategies for thermal states with probabilistic quantum metrology

TL;DR

This paper introduces a probabilistic measurement protocol that enhances the information-cost ratio for temperature estimation in thermal states, surpassing standard strategies by leveraging single-photon subtraction.

Contribution

It presents a novel post-selection method for thermal states that improves the information efficiency in quantum temperature estimation, focusing on classical states.

Findings

Achieves higher information-cost ratio than standard methods

Demonstrates effectiveness with classical thermal states

Connects classicality with the limits of post-selection advantages

Abstract

In probabilistic quantum metrology, one aims at finding weak measurements that concentrate the Fisher Information on the resulting quantum states, post-selected according to the weak outcomes. Though the Quantum Cram\'er-Rao bound itself cannot be overshot this way, it could be possible to improve the information-cost ratio, or even the total Fisher Information. We propose a post-selection protocol achieving this goal based on single-photon subtraction onto a thermal state of radiation yielding a greater information-cost ratio for the temperature parameter with respect to the standard strategy required to achieve the Quantum Cram\'er-Rao bound. We address just fully-classical states of radiation: this contrasts with (but does not contradict) a recent result proving that, concerning unitary quantum estimation problems, post-selection strategies can outperform direct measurement protocols only if a particular quasiprobability associated with the family of parameter-dependent quantum states becomes negative, a clear signature of nonclassicality.