Multiparameter estimation with single photons

It was suggested in [Phys. Rev. Lett. 111, 070403] that optical networks with relatively simple preparation and measurement devices -- single photon Fock states and on-off detectors -- can show significant improvements over classical strategies for multiparameter estimation when the number of modes in the network is small.~ This was further developed in [arXiv:1610.07128] for the case of single parameter estimation, and shown to be sub-shotnoise only for n\textless 7. ~In this paper, we show that this simple strategy can give asymptotically post-classical sensitivity for multiparameter estimation even when the number of modes is large.~ Additionally, we consider the effects of several other measurement techniques that can increase the efficiency of this device.