Work Extraction from Unknown Quantum Sources

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery.

Automated summary

Energy extraction is an important task in thermodynamics. In quantum physics, ergotropy is used to measure the extractable work under cyclic Hamiltonian control. However, existing methods require perfect knowledge of the initial state, which is not applicable to unknown or untrusted quantum sources. The authors propose a new notion of ergotropy that can be applied when only limited knowledge of the quantum states is available.