Temporal coherence of optical fields in the presence of entanglement

In classical coherence theory, coherence time is typically related to the bandwidth of the optical field. Narrowing the bandwidth will result in the lengthening of the coherence time. This will erase temporal distinguishability of photons due to time delay in pulsed photon interference. However, this is changed in an SU(1,1)-type quantum interferometer where quantum entanglement is involved. In this paper, we investigate how the temporal coherence of the fields in a pulse-pumped SU(1,1) interferometer changes with the bandwidth of optical filtering. We find that, because of the quantum entanglement, the coherence of the fields does not improve when optical filtering is applied, in contrary to the classical coherence theory, and quantum entanglement plays a crucial role in quantum interference in addition to distinguishability.