Information and coherence as resources for work extraction from unknown quantum state and providing quantum advantages

TL;DR

This paper explores how information and quantum coherence serve as resources for extracting work from unknown quantum states without heat baths, revealing that coherence enables quantum advantages in work extraction.

Contribution

It introduces observational ergotropy as a measure of work extractable with partial information and shows coherence as a key resource for quantum advantage in this context.

Findings

Observational ergotropy decreases with classical post-processing.

Maximizing observational ergotropy recovers standard ergotropy.

Quantum coherence in measurements enables work extraction beyond classical limits.

Abstract

The amount of extractable work from a physical system is fundamentally connected to the information available about its state, as illustrated by Maxwell's demon and the Gibbs paradox. In standard thermodynamic protocols involving system--bath interactions, the maximum work is given by the free-energy difference between the initial state and the corresponding Gibbs state at the bath temperature. This motivates a natural question: does information also limit work extraction in closed quantum systems that do not involve a heat bath and where work is obtained through unitary operations generated by a time-dependent Hamiltonian? While ergotropy quantifies the maximum work extractable via unitary operations, it assumes complete knowledge of the quantum state, typically requiring full state tomography. In realistic scenarios, however, only partial information is accessible. In this case, the relevant figure of merit is observational ergotropy, which depends explicitly on the measurement used to probe the system. We show that observational ergotropy decreases under classical post-processing of measurement outcomes, implying that fine-grained measurements allow greater work extraction than coarse-grained ones. Moreover, maximizing observational ergotropy over all possible measurements recovers standard ergotropy, which decomposes into incoherent (classical) and coherent (quantum) contributions. Our results demonstrate that coherence in the measurement projectors constitutes the key resource, enabling work extraction beyond the incoherent limit and establishing coherence as the origin of quantum advantage in observational ergotropy extraction.