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Quantum frequency up-conversion is a cutting-edge technique that leveragesthe interaction between photons and quantum systems to shift the frequency ofsingle photons from a lower frequency to a higher frequency. If the photonbefore up-conversion was one of the entangled pair, then it is important tounderstand how much entanglement is preserved after up-conversion. In thisstudy, we present a theoretical analysis of the transformation of thetime-dependent second-order quantum correlations in photon pairs and find thepreservation of such correlations under fairly general conditions. We alsoanalyze the two-photon Hong-Ou-Mandel interference between thefrequency-converted idler photon and the signal photon. The visibility of thetwo-photon interference is sensitive to the magnitude of the frequencyconversion, and it improves when the frequency separation between two photonsgoes down.

Two-photon Hong-Ou-Mandel interference and quantum entanglement between the frequency-converted idler photon and the signal photon