Photon pairs produced by parametric down-conversion or four-wave mixing caninterfere with each other in multiport interferometers, or carry entanglementbetween distant nodes for use in entanglement swapping. This requires thephotons be spectrally pure to ensure good interference, and have high heraldingefficiency to know accurately the number of photons involved and to maintainhigh rates as the number of photons grows. Spectral filtering is often used toremove noise and define spectral properties. For heralded single photons highpurity and heralding efficiency is possible by filtering the heralding arm, butwhen both photons in typical pair sources are filtered, we show that theheralding efficiency of one or both of the photons is strongly reduced even byideal spectral filters with 100% transmission in the passband: any improvementin reduced-state spectral purity from filtering comes at the cost of loweredheralding efficiency. We consider the fidelity to a pure, lossless singlephoton, symmetrize it to include both photons of the pair, and show thisquantity is intrinsically limited for sources with spectral correlation. Wethen provide a framework for this effect for benchmarking common photon pairsources, and present an experiment where we vary the photon filter bandwidthsand measure the increase in purity and corresponding reduction in heraldingefficiency.
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