Is coherence catalytic?

Quantum coherence, the ability to control the phases in superposition states is a resource, and it is of crucial importance, therefore, to understand how it is consumed in use. It has been suggested that catalytic coherence is possible, that is repeated use of the coherence without degradation or reduction in performance. The claim has particular relevance for quantum thermodynamics because, were it true, it would allow free energy that is locked in coherence to be extracted indefinitely. We address this issue directly with a careful analysis of the proposal by Åberg (2014 Phys. Rev. Lett. 113 150402). We find that coherence cannot be used catalytically, or even repeatedly without limit