Limits on the heralding efficiencies and spectral purities of spectrally-filtered single photons from photon pair sources

Understand

Photon pairs produced by parametric down-conversion or four-wave mixing can interfere with each other in multiport interferometers, or carry entanglement between distant nodes for use in entanglement swapping.

• This requires the photons be spectrally pure to ensure good interference, and have high heralding efficiency to know accurately the number of photons involved and to maintain high rates as the number of photons grows.
• Spectral filtering is often used to remove noise and define spectral properties.
• For heralded single photons high purity and heralding efficiency is possible by filtering the heralding arm, but when both photons in typical pair sources are filtered, we show that the heralding efficiency of one or both of the photons is strongly reduced even by ideal spectral filters with 100% transmission in the passband: any improvement in reduced-state spectral purity from filtering comes at the cost of lowered heralding efficiency.