Quantifying coherence in infinite-dimensional systems

We investigate the quantification of coherence in the infinite-dimensional systems, and especially, we focus on the infinite-dimensional bosonic systems in the Fock space. We find that given the average energy constraints, the relative entropy of coherence serves as a well-defined quantification of coherence in the infinite-dimensional systems, however, the l(1) norm of coherence fails. Via using the relative entropy of coherence as the quantification of coherence, we generalize the case to multimode Fock spaces, and some 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.