  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.
