Alternative measures of uncertainty in quantum metrology: Contradictions and limits

TL;DR

This paper investigates various intrinsic measures of uncertainty in quantum metrology, revealing contradictions and limits in their conclusions, and compares these with actual estimation errors after measurements.

Contribution

It introduces a family of uncertainty measures based on probability distributions and analyzes their implications in quantum metrology, highlighting contradictions among different measures.

Findings

Different measures lead to contradictory conclusions.

Some measures suggest arbitrarily small uncertainty with fixed resources.

Intrinsic measures can differ significantly from actual estimation errors.

Abstract

We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of minute changes of physical quantities. We show that different measures lead to contradictory conclusions, including the possibility of arbitrarily small uncertainty for fixed resources. These intrinsic performances are compared with the averaged error in the corresponding estimation problem after single-shot measurements.