Which role does multiphoton interference play in small phase estimation in quantum Fourier transform interferometers?

TL;DR

This paper investigates the impact of multiphoton interference on phase sensitivity in quantum Fourier transform interferometers, revealing that interference provides only a constant enhancement for small phase values, regardless of photon distinguishability.

Contribution

It demonstrates that multiphoton interference offers a limited, constant factor improvement in phase sensitivity for small phases, independent of photon number or phase weights.

Findings

Interference enhances phase sensitivity by a constant factor for small phases.

Enhancement arises from interference of polynomially many multiphoton path amplitudes.

Results are independent of photon number and phase weight factors.

Abstract

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.