  Coherence, a strictly quantum phenomenon, has found many applications, from
quantum information theory and thermodynamics to quantum foundations and
biology. When physical constraints are taken into consideration creation of
coherence in a system is usually impossible and must therefore be extracted
from another system acting as a reservoir. In this article we present two
faithful extraction protocols in the sense that the interaction involved
between the system and reservoir is coherence preserving. As an example we
implement both in the case where the reservoir is a quantum harmonic oscillator
in a coherent and a squeezed state respectively, and study the limits of
repeatable extraction. For a single extraction onto qubits it is demonstrated
that, perhaps surprisingly, one of the protocols manages to outperform a
previous method, known as catalytic coherence, which allows the creation of an
extra amount of coherence between degenerate energy eigenstates of the combined
system.
