Squeezing-Enhanced Two-Phase Estimation with N-Particle W-type States

TL;DR

This paper demonstrates that optical parametric amplification enhances multiparameter phase estimation precision in interferometers, with robustness against moderate photon loss, by amplifying intra-mode photon correlations.

Contribution

It provides an analytical framework for understanding OPA's role in quantum metrology and shows its advantage in realistic noisy conditions.

Findings

OPA significantly improves phase estimation precision in lossless interferometers.

Enhancement is due to amplification of intra-mode photon-number correlations.

OPA-assisted scheme remains advantageous under moderate photon loss.

Abstract

We investigate the simultaneous estimation of two optical phases in a three-mode interferometer assisted by optical parametric amplification (OPA). By employing the normally ordered characteristic-function formalism, we analytically obtain all photon-number moments of the output quantum state, enabling an explicit evaluation of the quantum Fisher information matrix for multiparameter phase estimation. In the lossless scenario, we show that uniformly applied OPA significantly enhances the attainable precision beyond that of an unamplified interferometer. By analyzing the second-order correlation functions, we demonstrate that this enhancement originates from the amplification of intra-mode photon-number correlations, rather than from inter-mode correlations. We further extend our analysis to realistic interferometers with photon loss using a purification-based variational approach. Although loss degrades the achievable precision, the OPA-assisted scheme retains a clear advantage for moderate loss, indicating a degree of robustness against dissipation. Our results clarify the physical mechanism underlying OPA-enhanced multiparameter quantum metrology and provide guidelines for optimizing phase estimation protocols in realistic noisy environments.