Performance-tradeoff relation for locating two incoherent optical point sources

TL;DR

This paper investigates the fundamental limits and tradeoffs in quantum measurements for estimating the position and separation of two incoherent optical point sources, revealing how optimal measurements must balance information extraction.

Contribution

It introduces an information-regret-tradeoff relation to characterize measurement incompatibility and guides the design of optimal measurement schemes for joint parameter estimation.

Findings

Optimal measurements for small separation sources prioritize separation information over centroid.

The tradeoff relation provides insights into measurement incompatibility and potential improvements.

Sequential measurement schemes can be optimized based on the tradeoff analysis.

Abstract

The optimal quantum measurements for estimating individual parameters might be incompatible with each other so that they cannot be jointly performed. The tradeoff between the estimation precision for different parameters can be characterized by information regret -- the difference between the Fisher information and its quantum limit. We show that the information-regret-tradeoff relation can give us not only an intuitive picture of the potential in improving the joint scheme of estimating the centroid and the separation, but also some clues to the optimal measurements for the sequential scheme. In particular, we show that, for two incoherent point sources with a very small separation, the optimal measurement for the separation must extract little information about the centroid, and vice versa.