Optimizing measurement tradeoffs in multiparameter spatial superresolution

TL;DR

This paper identifies optimal measurement strategies for jointly estimating the centroid and separation of two incoherent point sources in quantum superresolution, balancing information tradeoffs to maximize total information in the small separation regime.

Contribution

It determines the optimal measurements for joint estimation in quantum superresolution, adaptable to tradeoffs between centroid and separation information for arbitrary point spread functions.

Findings

Optimal measurements for joint estimation are derived.

Measurement tradeoffs enable more information extraction.

Total information can be maximized within the tradeoff set.

Abstract

The quantum Cram\'er-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same time are not known. In this work, we ascertain these optimal measurements for an arbitrary point spread function, in the most relevant regime of a small separation between the sources. Our measurement can be adjusted within a set of tradeoffs, allowing more information to be extracted from the separation or the centroid while ensuring that the total information is the maximum possible.