# 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.