Faithful extraction of quantum coherence

Extraction of quantum coherence plays an important role in the theory of quantum information and thermodynamics. We introduce a new type of extraction protocol based on the sub-swap operation between the extracted system and the system which acts as a source of coherence. By implementing it for a source in the Glauber state of a harmonic oscillator we investigate the conditions under which catalysis of coherence, i.e., repeatable extraction, is possible and discuss the limits of repeatability in the general case. By comparing the protocol with others in the literature we demonstrate that although by construction no extra amount of coherence in the combined system is created, it manages to extract more coherence in a qubit than previously possible.