Optimal State Preparation for Impulse Estimation in Gaussian Quantum Systems

TL;DR

This paper introduces an optimal control approach to improve impulse disturbance estimation in Gaussian quantum systems by dynamically shaping estimation covariances, outperforming traditional methods.

Contribution

It develops a nonlinear optimal control framework for state preparation that enhances impulse estimation in quantum systems, surpassing conventional modulation techniques.

Findings

Reduces estimation variance by up to a factor of two in nanomechanical systems.

Maximizes information gain at known impulse times through dynamic covariance shaping.

Differs from traditional squeezing protocols by avoiding degradation of impulse inference.

Abstract

We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for linear Gaussian systems to collect information from the temporal vicinity of the disturbance, we cast the minimization of disturbance estimation uncertainty as a nonlinear optimal control problem over time-dependent system parameters. The resulting method dynamically shapes the estimation covariances through parametric modulation, maximizing information gain at a known impulse time. This differs fundamentally from conventional squeezing protocols using periodic modulation that effectively degrade inference of impulse-like disturbances. Applied to nanomechanical resonators and levitated nanoparticles, optimal parametric driving reduces estimation variance by up to a factor of two relative to steady-state operation