Equivalence of thermal-battery and sharp work-storage models with nonzero error

Determine whether the equivalence between the thermal-battery model and the sharp work-storage model established for exact work extraction persists when the fidelity error is nonzero.

Background

The paper studies work-extraction reliability using the thermal-battery model of Watanabe et al., in which a two-level battery is transformed into a pure excited state under thermal operations. The cited result establishes an equivalence between this model and a sharp work-storage model for exact extraction. The authors explicitly state that it is unresolved whether the equivalence continues to hold when extraction is allowed to have nonzero fidelity error, and therefore retain the thermal-battery formulation throughout their analysis.