Optimal estimation of conjugate shifts in position and momentum by classically correlated probes and measurements

TL;DR

This paper demonstrates that classical correlations between Gaussian probe states and measurements can achieve optimal simultaneous estimation of position and momentum shifts, offering a more feasible alternative to quantum entangled probes.

Contribution

It introduces a method using classically correlated Gaussian states for optimal conjugate parameter estimation, replacing the need for complex quantum entanglement.

Findings

Classical correlations can match quantum entanglement in estimation precision.

Feasible Gaussian state protocols can be used for force sensing.

The approach simplifies implementation of multi-parameter quantum sensing.

Abstract

Multi-parameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position and momentum. Designing quantum probes that allow simultaneous estimation of all parameters is therefore an important task. The optimal methods for estimation of the conjugate changes of position and momentum of quantum harmonic oscillator employ probes in entangled or quantum non-Gaussian states. We show that the same results can be obtained in a significantly more feasible fashion by employing independent sets of differently squeezed Gaussian states classically correlated to position or momentum measurements. This result demonstrates an unexplored power of a classical correlation between the probe states and measurements directly applicable to force sensing