Enhanced estimation of loss in the presence of Kerr nonlinearity

TL;DR

This paper demonstrates that Kerr nonlinearity can significantly improve the precision of loss estimation in dissipative bosonic channels, especially for short interaction times and moderate media sizes, using Gaussian probes.

Contribution

It provides a detailed analysis of how Kerr nonlinearity enhances quantum Fisher information for loss estimation and identifies optimal nonlinearity parameters for different conditions.

Findings

Kerr nonlinearity improves estimation precision for short interactions.

Optimal nonlinearity values depend on interaction time and input parameters.

Enhancement is not directly related to non-Gaussianity of probes.

Abstract

We address the characterization of dissipative bosonic channels and show that estimation of the loss rate by Gaussian probes (coherent or squeezed) is improved in the presence of Kerr nonlinearity. In particular, enhancement of precision may be substantial for short interaction time, i.e. for media of moderate size, e.g. biological samples. We analyze in detail the behaviour of the quantum Fisher information (QFI), and determine the values of nonlinearity maximizing the QFI as a function of the interaction time and of the parameters of the input signal. We also discuss the precision achievable by photon counting and quadrature measurement and present additional results for truncated, few-photon, probe signals. Finally, we discuss the origin of the precision enhancement, showing that it cannot be linked quantitatively to the non-Gaussianity of the interacting probe signal.