To fully utilize the energy-time degree of freedom of photons for opticalquantum information processes, it is necessary to control and characterize thequantum states of the photons at extremely short time scales. For measurementsbeyond the time resolution of available detectors, two-photon interference witha photon in a short time reference pulse may be a viable alternative. In thispaper, we derive the temporal measurement operators for the bunching statisticsof a single photon input state with a reference photon. It is shown that theeffects of the pulse shape of the reference pulse can be expressed in terms ofa spectral filter selecting the bandwidth within which the measurement can betreated as an ideal projection on eigenstates of time. For full quantumtomography, temporal coherence can be determined by using superpositions ofreference pulses at two different times. Moreover, energy-time entanglement canbe evaluated based on the two-by-two entanglement observed in the coherencesbetween pairs of detection times.
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