Adaptive Continuous Homodyne Phase Estimation Using Robust Fixed-Interval Smoothing

TL;DR

This paper demonstrates how combining a Rauch-Tung-Striebel smoother with an optimal Kalman filter in adaptive homodyne phase estimation can reduce mean-square error below the standard quantum limit and enhance robustness to noise uncertainties.

Contribution

It introduces a robust fixed-interval smoothing approach for adaptive quantum phase estimation, improving accuracy and robustness over existing methods.

Findings

Mean-square error below standard quantum limit achieved

Robust smoothing enhances estimation accuracy under parameter uncertainties

Integration of Rauch-Tung-Striebel smoother with Kalman filter proven effective

Abstract

Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or nonadaptive estimation using filtering alone. Here, we illustrate how the mean-square error in the adaptive phase estimate may be further reduced below the standard quantum limit for the stochastic noise process considered by using a Rauch-Tung-Striebel smoother as the estimator, alongwith an optimal Kalman filter in the feedback loop. Further, the estimation using smoothing can be made robust to uncertainties in the underlying parameters of the noise process modulating the system phase to be estimated. This has been done using a robust fixed-interval smoother designed for uncertain systems satisfying a certain integral quadratic constraint.