Entanglement-enhanced fluctuation-free daemonic ergotropy with random measurements

Abstract

Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.

7+10 pages, 2 figures