  We study distinguishability of photons in multiphoton interference on a
multiport when fast detectors, capable of precise time resolution, are
employed. Such a setup was previously suggested for experimental realization of
boson sampling with single photons. We investigate if fast photodetection
allows to circumvent distinguishability of realistic single photons in mixed
states. To this goal we compare distinguishability of photons in two setups:
(a) with photons in the same average (temporal) profile on a spatial
interferometer and photodetection incapable of (or with strongly imprecise)
time resolution and (b) with photons in generally different average temporal
profiles on the same spatial interferometer and photodetection with precise
time resolution. Exact analytical results are obtained for Gaussian-shaped
single photons with Gaussian distribution of photon arrival time.
Distinguishability of photons in the two setups is found to be strikingly
similar. For the same purity of photon states, only the same quality
experimental boson sampling can be achieved using either of the two setups. The
upshot of our results is that distinguishability due to mixed states is an
intrinsic property of photons, whatever the photodetection scheme.
