Multiparameter Gaussian Quantum Metrology

TL;DR

This paper derives analytical formulas for quantum Fisher information in Gaussian quantum metrology, demonstrating optimal joint parameter estimation in optical interferometry with advantages over separate measurements.

Contribution

It provides the first general analytical expressions for quantum Fisher information and measurement compatibility in multimode Gaussian states for multi-parameter estimation.

Findings

Two-mode displaced squeezed probes enable simultaneous estimation of phase and noise parameters.

Optimal tuning of squeezing and displacement improves measurement compatibility.

Joint estimation outperforms individual estimation as probe energy increases.

Abstract

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfil the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.