Average number is an insufficient metric for interferometry

TL;DR

This paper challenges the reliance on average particle number as a metric in interferometry, showing it can misrepresent the effective particle usage and metrological advantage.

Contribution

It demonstrates that average particle number can be decoupled from useful particle count in various states within both frequentist and Bayesian frameworks.

Findings

Average particle number does not always reflect effective particle usage.

Metrological advantage can be independent of the average number.

The paper clarifies the limitations of using average particle count as a metric.

Abstract

We argue that analysing schemes for metrology solely in terms of the average particle number can obscure the number of particles effectively used in informative events. For a number of states we demonstrate that, in both frequentist and Bayesian frameworks, the average number of a state can essentially be decoupled from the aspects of the total number distribution associated with any metrological advantage.