Precision bounds for noisy nonlinear quantum metrology

TL;DR

This paper establishes fundamental limits on the precision of nonlinear quantum measurements under noise, showing that second-order schemes are similarly affected by photon loss and phase diffusion as linear ones, with potential for environmental engineering to enhance performance.

Contribution

It derives the ultimate precision bounds for nonlinear quantum metrology schemes in noisy environments, highlighting their similarities to linear schemes and potential for performance improvement through environment control.

Findings

Second-order estimation schemes are similarly affected by noise as linear schemes.

The phase sensitivity gain is limited to an $ ext{O}(1/N)$ factor under noise.

Environmental engineering can potentially improve measurement performance under phase diffusion.

Abstract

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon loss and phase diffusion. We find that the second-order estimation scheme is affected by both types of noise in an analogous way as the linear one. Moreover, we observe that for both types of noise the gain in the phase sensitivity with respect to the linear estimation scheme is given by a multiplicative term $\mathcal{O}(1/N)$. Interestingly, we also find that under certain circumstances, a careful engineering of the environment can, in principle, improve the performance of measurement schemes affected by phase diffusion.