Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles

TL;DR

This paper extends quantum metrology concepts to states with fluctuating particle numbers, analyzing how entanglement and sensitivity are affected in realistic experiments with particle number uncertainties.

Contribution

It generalizes the theory of quantum phase estimation and entanglement to include states with classical and quantum particle number fluctuations.

Findings

Entanglement and spin-squeezing are characterized in fluctuating particle number states.

The analysis applies to most current precision measurement experiments with uncertain particle counts.

Theoretical framework accommodates classical and quantum particle number fluctuations.

Abstract

The concepts of separability, entanglement, spin-squeezing and Heisenberg limit are central in the theory of quantum enhanced metrology. In the current literature, these are well established only in the case of linear interferometers operating with input quantum states of a known fixed number of particles. This manuscript generalizes these concepts and extends the quantum phase estimation theory by taking into account classical and quantum fluctuations of the particle number. Our analysis concerns most of the current experiments on precision measurements where the number of particles is known only in average.