Resource theory in which observational ergotropic advantage is monotonic

Determine under which resource theory of measurement coherence the observational ergotropic advantage quantifier is a monotone.

Background

The paper introduces observational ergotropic advantage as a state-independent quantifier of the excess work extractable using a quantum measurement beyond the maximum achievable with incoherent measurements. Although the quantifier is shown to be tightly bounded by established measures of measurement coherence, including robustness and the l∞-norm measure, the paper also demonstrates that it is not monotonic with robustness and fails to be monotonic even under physically incoherent operations (PIO).

Consequently, the authors leave unresolved the identification of a resource-theoretic framework—possibly involving a different choice of free operations or resource theory—in which observational ergotropic advantage satisfies the monotonicity requirement for a coherence measure. This question is explicitly presented as the first immediate research direction.