Multiparameter estimation with single photons—linearly-optically generated quantum entanglement beats the shotnoise limit

It was suggested in (Motes et al 2015 Phys. Rev. Lett. 114 170802) that optical networks with relatively inexpensive overheads—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 (). A similar case was made in (Humphreys et al 2013 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 Cramer–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.