Quantum work extraction from partial information and with finite resources
Information can be converted into work, but in quantum mechanics information about a state is not freely available: it must be inferred statistically from measurements on a finite number of copies. We study work extraction in this finite-resource setting by introducing a partial-information and finite-resources (PIFR) quantum Maxwell's demon. Given $N$ identical copies of a state with known Hamiltonian, the demon measures $M$ copies to estimate the state and the corresponding ergotropic unitary, which is then applied to the remaining $N-M$ copies. This protocol induces a trade-off between information acquisition, reconstruction accuracy, and thermodynamic yield, making the total extracted work normalized to the ideal ergotropic benchmark the relevant figure of merit. As our central result, we derive a universal closed-form trade-off bound that places this ergotropic efficiency between a Carnot-type ceiling $1-M/N$ and a floor controlled by a reconstruction precision rooted in finite-sample quantum estimation theory; optimizing the copy allocation yields $M^*\propto N^{2/3}$ and an $N^{-1/3}$ approach to the ideal limit, set by a conservative, worst-case reconstruction precision. By considering standard quantum state tomography, we numerically verify the presence of an optimal resource distribution, which also depends on the purity of the state under consideration. Our results identify finite-copy work extraction as a genuinely task-dependent inference problem, in which estimation strategies should be judged by thermodynamic performance rather than reconstruction fidelity alone.