Globally optimal interferometry with lossy twin Fock probes - Volkoff, T. J.; Ryu, Changhyun (Frontiers in Physics, 2024)
Parity or quadratic spin (e.g., J 2 z ) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the J 2 z readout is restricted to an o( √ N ) occupation imbalance. We show that a method of moments readout of two quadratic spin observables J 2 z and J 2 + + J 2 -is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all θ. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states,showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four mode state | N 4 , N 4 , N 4 , N 4 ⟩ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases θ 1 , θ 2 (compared to independent probing of the MZ phases by two copies of | N 4 , N 4 ⟩) appears when more than one particle is lost.