Globally optimal interferometry with lossy twin Fock probes.

Parity or quadratic spin (e.g., J²_z) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating 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 J²_z readout is restricted to an o(√N) occupation imbalance. We show that a method of moments readout of two quadratic spin observables J²_z and J²₊ + J²_- 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 TF states, showing that the 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 the estimation of any linear function of the local MZ phases θ₁ and θ₂ (compared to independent probing of the MZ phases by two copies of |N/4, N/4〉) appears when more than one particle is lost. [ABSTRACT FROM AUTHOR]