Fig. 10: Ultimate bounds on precision in lossy photonic interferometry with dark counts and local unitary control.

The solid and dotted blue lines are the inverse of the finite-N (evaluated via an SDP) and asymptotic (see Eq. (53)) CE bounds, respectively, for detection efficiency η = 0.9 and dark-count rate \({\mathsf{p}}=0.1\). Control gates may act on each individual dual-rail photon. For comparison, we also plot, solid and dotted black lines, the corresponding quantities when only photon loss is present (η = 0.9, \({\mathsf{p}}\) = 0).