Quantum optical metrology in the lossy $SU(2)$ and $SU(1,1)$ interferometers

TL;DR

This paper analyzes phase sensitivity in lossy $SU(2)$ and $SU(1,1)$ interferometers using quantum Cramér-Rao bound, showing near-optimal performance with homodyne detection despite photon loss.

Contribution

It explicitly constructs optimal detection schemes and demonstrates robustness of homodyne detection in lossy conditions for these interferometers.

Findings

Homodyne detection nearly achieves optimal phase sensitivity under photon loss.

The effects of imperfect detectors cannot be mitigated by increasing amplifier gain for certain states.

Both $SU(2)$ and $SU(1,1)$ interferometers perform well with proper detection schemes in lossy environments.

Abstract

We study the phase sensitivity in the conventional $SU(2)$ and nonconventional $SU(1,1)$ interferometers with the coherent and squeezed vacuum input state via the quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections, are nearly optimal. We also find that unlike the coherent state and squeezed vacuum state, the effects of the imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic coherent-squeezed state by increasing the amplifier gain of the OPA.