Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators

TL;DR

This paper investigates the fundamental limits of simultaneously estimating loss and nonlinearity in driven-dissipative Kerr resonators, revealing conditions under which joint estimation is optimal and analyzing measurement strategies.

Contribution

It demonstrates that the driven-dissipative Kerr model is asymptotically classical for joint parameter estimation and evaluates the performance of quadrature detection.

Findings

Quantum Fisher information increases with interaction time and driving amplitude.

The model is asymptotically classical, allowing joint estimation without quantum noise.

Quadrature detection oscillates in Fisher information, approaching the quantum limit.

Abstract

We address multiparameter quantum estimation for coherently driven nonlinear Kerr resonators in the presence of loss. In particular, we consider the realistic situation in which the parameters of interest are the loss rate and the nonlinear coupling, whereas the amplitude of the coherent driving is known and externally tunable. Our results show that this driven-dissipative model is asymptotically classical, i.e. the Uhlmann curvature vanishes, and the two parameters may be jointly estimated without any additional noise of quantum origin. We also find that the ultimate bound to precision, as quantified by the quantum Fisher information (QFI), increases with the interaction time and the driving amplitude for both parameters. Finally, we investigate the performance of quadrature detection, and show that for both parameters the Fisher information oscillates in time, repeatedly approaching the corresponding QFI.