Multiple-phase quantum interferometry -- real and apparent gains of measuring all the phases simultaneously

TL;DR

This paper analyzes the true quantum advantages in multiple-phase interferometry, showing that simultaneous estimation offers a constant factor improvement over separate estimation, challenging previous claims of better scaling.

Contribution

It provides an operational characterization of quantum gains in multi-phase interferometry and clarifies the limitations of quantum Fisher information-based analysis.

Findings

Optimal simultaneous estimation yields a constant factor precision improvement.

Contrary to prior claims, no better than constant scaling with the number of phases.

Highlights the insufficiency of quantum Fisher information alone for analyzing quantum advantages.

Abstract

We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the advantage of the optimal simultaneous estimation scheme amounts to a constant factor improvement when compared with schemes where each phase is estimated separately -- contrary to a widely cited results claiming a better precision scaling in terms of the number of phases involved.