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We develop general tools to characterise and efficiently compute relevantobservables of multimode $N$-photon states generated in non-linear decays inone-dimensional waveguides. We then consider optical interferometry in aMach-Zender interferometer where a $d$-mode photonic state enters in each armof the interferometer. We derive a simple expression for the Quantum FisherInformation in terms of the average photon number in each mode, and show thatit can be saturated by number-resolved photon measurements that do notdistinguish between the different $d$ modes.

Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology