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Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements. 

When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments. 

The theory of sum-frequency generation (SFG) as a two-photon measurement process is used to infer the role of two-photon entanglement in this process, and an experimental setup and preliminary data are presented as a way towards quantifying the dependence of SFG on entanglement.