We develop general tools to characterise and efficiently compute relevant observables of multimode N-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a d-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different d modes.
@article{arxiv.1910.03323,
title = {Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology},
author = {M. Perarnau-Llobet and A. González-Tudela and J. I. Cirac},
journal= {arXiv preprint arXiv:1910.03323},
year = {2020}
}