All coherent measurements provide observational ergotropic advantage

Abstract: The use of quantum resources in the work extraction from a quantum system is an emerging research topic. Recently, [arXiv:2602.22893] established the necessity of measurement coherence for obtaining advantage in work extraction from an unknown isolated quantum system. However, a quantitative relation between the magnitude of this advantage and established measures of measurement coherence is missing. Here, we establish such a connection by introducing a faithful operational quantifier of the work advantage provided by a measurement. We show that measurement coherence is necessary and sufficient for a positive advantage, and derive upper and lower bounds in terms of the robustness of measurement coherence and an $l_{\infty}$ norm based coherence measure respectively. Finally, we examine this quantifier of advantage from the resource theoretic perspective. Our results provide an operational characterisation of measurement coherence as a resource for work extraction and reveal a nontrivial relation between its resource content and thermodynamic value.