Which role does multiphoton interference play in small phase estimation in quantum Fourier transform interferometers?. (arXiv:1712.01898v1 [quant-ph])

Recently, quantum Fourier transform interferometers have been demonstrated to
allow a quantum metrological enhancement in phase sensitivity for a small
number n of identical input single photons [1-3]. However, multiphoton
distinguishability at the detectors can play an important role from an
experimental point of view [4]. This raises a fundamental question: How is the
phase sensitivity affected when the photons are completely distinguishable at
the detectors and therefore do not interfere? In other words, which role does
multiphoton interference play in these schemes? Here, we show that for small
phase values the phase sensitivity achievable in the proposed schemes with
indistinguishable photons is enhanced only by a constant factor with respect to
the case of completely distinguishable photons at the detectors. Interestingly,
this enhancement arises from the interference of only a polynomial number (in
n) of the total n! multiphoton path amplitudes in the n-port interferometer.
These results are independent of the number n of single photons and of the
phase weight factors employed at each interferometer channel.

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