It was suggested in Ref. [Phys. Rev. Lett. 114, 170802] that optical networks with relatively inexpensive overhead---single photon Fock states, passive optical elements, and single photon detection---can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small (n < 7). A similar case was made in Ref. [Phys. Rev. Lett. 111, 070403] for multi-parameter estimation, where measurement is instead made using photon-number resolving detectors. In this paper, we analytically compute the quantum Cram\'er-Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, we provide a simplified measurement scheme using only single-photon (on-off) detectors that is capable of approximately obtaining this sensitivity for a small number of modes.
@article{arxiv.1706.05492,
title = {Multiparameter estimation with single photons},
author = {Chenglong You and Sushovit Adhikari and Yuxi Chi and Margarite L. LaBorde and Corey T. Matyas and Chenyu Zhang and Zuen Su and Tim Byrnes and Chaoyang Lu and Jonathan P. Dowling and Jonathan P. Olson},
journal= {arXiv preprint arXiv:1706.05492},
year = {2020}
}