Globally optimal interferometry with lossy twin Fock probes

TL;DR

This paper develops globally optimal measurement strategies for quantum interferometry using twin Fock and Dicke states, accounting for particle loss, and demonstrates advantages in distributed phase estimation.

Contribution

It introduces a method of moments readout for Dicke states that is globally optimal and extends analysis to lossy scenarios, improving quantum phase estimation strategies.

Findings

Method of moments readout saturates QFI for all phases.

Optimal estimation is achievable with four observables under loss.

Distributed interferometry shows advantage when particles are lost.

Abstract

Parity or quadratic spin (e.g., $J_{z}^{2}$) 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 $\theta$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $\theta=0$, whereas better-than-standard quantum limit performance of the $J_{z}^{2}$ readout is restricted to an $o(\sqrt{N})$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_{z}^{2}$ and $J_{+}^{2}+J_{-}^{2}$ is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all $\theta$. 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 $\theta$ 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 $\vert {N\over 4},{N\over 4},{N\over 4},{N\over 4}\rangle$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases $\theta_{1}$, $\theta_{2}$ (compared to independent probing of the MZ phases by two copies of $\vert {N\over 4},{N\over 4}\rangle$) appears when more than one particle is lost.