Robustness of quantum Fourier transform interferometry

We analyse the effect of decoherence and noise on quantum Fourier transform interferometry, in which a boson sampling photonic network is used to measure optical phase gradients. This novel type of metrology is shown to be robust against phase decoherence. One can also measure gradients using lower order correlations without substantial degradation. Our results involve estimation of up to a 100 x 100 matrix permanent.