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Quantifying Coherence in Infinite Dimensional Systems

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.