  We study the quantification of coherence in infinite dimensional systems,
especially the infinite dimensional bosonic systems in Fock space. We show that
given the energy constraints, the relative entropy of coherence serves as a
well-defined quantification of coherence in infinite dimensional systems. Via
using the relative entropy of coherence, we also generalize the problem to
multi-mode Fock space and special examples are considered. It is shown that
with a finite average particle number, increasing the number of modes of light
can enhance the relative entropy of coherence. With the mean energy constraint,
our results can also be extended to other infinite-dimensional systems.
