Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit

TL;DR

This paper determines the optimal Gaussian input state and measurement strategy for estimating parameters in multimode passive linear optical circuits, achieving ultimate precision bounds with fixed probe photon number.

Contribution

It identifies the optimal single-mode squeezed vacuum input and homodyne detection for Gaussian metrology in multimode circuits, including strategies with multiple circuits and passive controls.

Findings

Optimal input state is a single-mode squeezed vacuum.

Homodyne measurement achieves ultimate precision.

Strategy extends to multiple circuits with passive controls.

Abstract

Bounds on the ultimate precision attainable in the estimation of a parameter in Gaussian quantum metrology are obtained when the average number of bosonic probes is fixed. We identify the optimal input probe state among generic (mixed in general) Gaussian states with a fixed average number of probe photons for the estimation of a parameter contained in a generic multimode interferometric optical circuit, namely, a passive linear circuit preserving the total number of photons. The optimal Gaussian input state is essentially a single-mode squeezed vacuum, and the ultimate precision is achieved by a homodyne measurement on the single mode. We also reveal the best strategy for the estimation when we are given $L$ identical target circuits and are allowed to apply passive linear controls in between with an arbitrary number of ancilla modes introduced.