Phase sensitivity bounds for two-mode interferometers

TL;DR

This paper derives fundamental bounds on phase estimation sensitivity in two-mode interferometers, considering particle number fluctuations and coherence effects, establishing conditions for reaching the Heisenberg limit.

Contribution

It provides general phase sensitivity bounds for two-mode interferometers with fluctuating particle numbers, highlighting the role of coherence and entanglement in surpassing shot noise limits.

Findings

Particle entanglement is necessary but not sufficient to beat shot noise.

Heisenberg limit is achievable under certain unbiased estimator conditions.

Coherence creation and detection influence phase sensitivity bounds.

Abstract

We provide general bounds of phase estimation sensitivity in linear two-mode interferometers. We consider probe states with a fluctuating total number of particles. With incoherent mixtures of state with different total number of particles, particle entanglement is necessary but not sufficient to overcome the shot noise limit. The highest possible phase estimation sensitivity, the Heisenberg limit, is established under general unbiased properties of the estimator. When coherences can be created, manipulated and detected, a phase sensitivity bound can only be set in the central limit, with a sufficiently large repetition of the interferometric measurement.