From Independent to Joint: Enhancing Quantum Phase and Correlation Factor Estimation by Squeezed Reservoir Engineering

TL;DR

This paper demonstrates how correlated squeezed-thermal reservoirs can be engineered to enhance the simultaneous estimation of quantum phase and correlation factors, emphasizing the importance of squeezing phase optimization for high-precision quantum sensing.

Contribution

It introduces optimal phase-matching conditions for joint estimation of phase and correlation parameters using squeezed reservoirs, advancing quantum metrology techniques.

Findings

Optimal squeezing phase conditions depend on the correlation factor μ.

Joint estimation achieves high precision by conserving quantum resources.

Phase-matching maximizes quantum Fisher information for both parameters.

Abstract

High-precision quantum parameter estimation is fundamental to the advancement of quantum metrology. Although reservoir engineering provides a powerful approach to improve estimation by tailoring system-environment interactions, the role of the squeezing phase and correlations arising from the sequential utilization of the same squeezed reservoir remains inadequately explored. In this work, we employ a correlated squeezed-thermal reservoir to enhance the precision of estimating the phase parameter $\phi$ and the correlation factor $\mu$, both individually and simultaneously. We show that the squeezing phase $\Phi$ is crucial for achieving quantum-enhanced precision, with optimal phase-matching conditions that depend strongly on $\mu$. Specifically, we derive the near-optimal phase-matching relations aimed at maximizing the quantum Fisher information (QFI) for both $\phi$ and $\mu$, as well as minimizing the total variance $\Delta_{\rm sim}$ in joint estimation. Furthermore, we show that the joint estimation variance is dominated by $F_{\phi}$, which motivates our search for the phase-matching conditions that minimize $\Delta_{\text{sim}}$. Through the ratio $R$ of variances, we demonstrate that joint estimation conserves quantum resources and maintains high precision when the squeezing phase is optimized for $F_{\phi}$, despite the inherent incompatibility of the parameters. These findings provide practical insights into reservoir engineering strategies for high-precision quantum sensing and information processing.