Heisenberg-scaling characterization of an arbitrary two-channel network via two-port homodyne detection

TL;DR

This paper introduces a practical Gaussian scheme using two-mode squeezed states and homodyne detection to achieve Heisenberg-scaling sensitivity in the simultaneous estimation of all parameters of an arbitrary two-channel unitary transformation, enabling advanced quantum metrology.

Contribution

It presents the first experimentally feasible method for Heisenberg-limited multiparameter estimation of two-channel networks using Gaussian states and homodyne detection.

Findings

Achieves Heisenberg-scaling sensitivity for all four parameters.

Saturates the multiparameter Cramér-Rao bounds with few measurements.

Applicable to calibration and sensing in integrated photonics.

Abstract

We present a fully Gaussian and experimentally feasible scheme for the simultaneous estimation of the four real parameters that characterize an arbitrary two-channel unitary transformation. The scheme utilizes a two-mode squeezed probe and balanced homodyne detection at both output ports, for which we derive the complete classical Fisher-information matrix analytically. Our scheme achieves the Heisenberg-scaling sensitivity for all four parameters simultaneously, enabling full multiparameter characterization of the generic two-channel interferometric device. We further show, by maximum-likelihood estimation, that the corresponding multiparameter Cram\'er-Rao bounds are saturated with a modest number of experimental repetitions and for low photon numbers. The scheme establishes a practical route to Heisenberg-scaling multiparameter Gaussian metrology for arbitrary two-channel networks, with direct relevance to calibration and sensing in integrated photonics and distributed quantum-enhanced measurement architectures.