Thermodynamic work cost of quantum estimation protocols

TL;DR

This paper analyzes the thermodynamic work costs involved in quantum estimation protocols, considering both multi-shot and single-shot scenarios, and explores how work constraints influence estimation precision.

Contribution

It introduces a comprehensive framework for quantifying thermodynamic work costs in quantum estimation, integrating both Shannon and min/max-entropy approaches.

Findings

Work cost can be quantified in both multi-shot and single-shot regimes.

Estimation precision depends on work constraints, with Fisher information and confidence intervals as key tools.

Single-shot protocols benefit from confidence intervals for reliable estimation.

Abstract

We discuss thermodynamic work cost of various stages of a quantum estimation protocol: probe and memory register preparation, measurement and extraction of work from post-measurement states. We consider both (i) a multi-shot scenario, where average work is calculated in terms of the standard Shannon entropy and (ii) a single-shot scenario, where deterministic work is expressed in terms of min- and max-entropies. We discuss an exemplary phase estimation protocol where estimation precision is optimized under a fixed work credit (multi-shot) or a total work cost (single-shot). In the multi-shot regime precision is determined using the concept of Fisher information, while in the single-shot case we advocate the use of confidence intervals as only they can provide a meaningful and reliable information in a single-shot experiment, combining naturally with the the concept of deterministic work.