Gaussian state interferometry with passive and active elements

TL;DR

This paper investigates the ultimate precision bounds of Gaussian-state optical interferometers with passive and active elements, demonstrating how detector efficiency impacts sensitivity and how active detection can restore Heisenberg scaling under loss.

Contribution

It provides a comprehensive analysis of quantum Fisher information bounds and shows how active detection can compensate for losses, improving interferometric sensitivity.

Findings

Heisenberg scaling achievable with ideal detectors and optimized Gaussian states.

Passive schemes' performance degrades with non-unit detector efficiency.

Active detection with optical parametric amplifiers restores Heisenberg scaling under loss.

Abstract

We address precision of optical interferometers fed by Gaussian states and involving passive and/or active elements, such as beam splitters, photodetectors and optical parametric amplifiers. We first address the ultimate bounds to precision by discussing the behaviour of the quantum Fisher information. We then consider photodetection at the output and calculate the sensitivity of the interferometers taking into account the non unit quantum efficiency of the detectors. Our results show that in the ideal case of photon number detectors with unit quantum efficiency the best configuration is the symmetric one, namely, passive (active) interferometer with passive (active) detection stage: in this case one may achieve Heisenberg scaling of sensitivity by suitably optimizing over Gaussian states at the input. On the other hand, in the realistic case of detectors with non unit quantum efficiency, the performances of passive scheme are unavoidably degraded, whereas detectors involving optical parametric amplifiers allow to fully compensate the presence of loss in the detection stage, thus restoring the Heisenberg scaling.