  To fully utilize the energy-time degree of freedom of photons for optical
quantum information processes, it is necessary to control and characterize the
quantum states of the photons at extremely short time scales. For measurements
beyond the time resolution of available detectors, two-photon interference with
a photon in a short time reference pulse may be a viable alternative. In this
paper, we derive the temporal measurement operators for the bunching statistics
of a single photon input state with a reference photon. It is shown that the
effects of the pulse shape of the reference pulse can be expressed in terms of
a spectral filter selecting the bandwidth within which the measurement can be
treated as an ideal projection on eigenstates of time. For full quantum
tomography, temporal coherence can be determined by using superpositions of
reference pulses at two different times. Moreover, energy-time entanglement can
be evaluated based on the two-by-two entanglement observed in the coherences
between pairs of detection times.
