Quantifying Coherence in Infinite Dimensional Systems

TL;DR

This paper investigates how to measure quantum coherence in infinite-dimensional systems like bosonic Fock space, demonstrating that energy constraints allow for a well-defined quantification using relative entropy, and exploring how coherence scales with system size.

Contribution

It introduces the use of relative entropy of coherence for infinite-dimensional systems under energy constraints and extends the analysis to multi-mode Fock spaces.

Findings

Relative entropy of coherence is well-defined under energy constraints.

Increasing the number of modes can enhance coherence with finite average particle number.

Results extend to other infinite-dimensional systems with mean energy constraints.

Abstract

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.