Quantum estimation through a bottleneck

TL;DR

This paper investigates quantum parameter estimation when measurement access is limited to one system, analyzing how generator properties and entanglement influence estimation precision.

Contribution

It establishes the continuity of quantum Fisher information with respect to generators and identifies conditions for optimal estimation under measurement bottlenecks.

Findings

Quantum Fisher information is continuous with respect to generators.

Conditions are derived for achieving maximum Fisher information despite bottlenecks.

Initial entanglement can enhance estimation performance.

Abstract

We study the estimation of a single parameter characterizing families of unitary transformations acting on two systems. We consider the situation with the presence of bottleneck, i.e. only one of the systems can be measured to gather information. The estimation capabilities are related to unitaries' generators. In particular, we establish continuity of quantum Fisher information with respect to generators. Furthermore, we find conditions on the generators to achieve the same maximum quantum Fisher information we would have in the absence of bottleneck. We also discuss the usefulness of initial entanglement across the two systems as well as across multiple estimation instances.