Invariance property of the Fisher information in scattering media

TL;DR

This paper reveals that, on average, the quantum Fisher information for measuring a sub-wavelength particle remains unaffected by complex scattering environments, except in the localization regime, impacting precision limits in nanophotonics.

Contribution

It demonstrates an invariance property of the mean quantum Fisher information in scattering media, linking environment complexity to measurement precision in quantum sensing.

Findings

Quantum Fisher information is unaffected by scattering environments on average.

Invariance breaks down in the Anderson localization regime.

Optimized input fields can achieve the mean quantum Fisher information.

Abstract

Determining the ultimate precision limit for measurements on a sub-wavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its complex environment. This invariance law breaks down only in the regime of Anderson localization, due to increased speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.