Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously

We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple phase interferometry and stress the 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, which is contrary to widely cited results claiming a better precision scaling in terms of the number of phases involved.

Automated summary

We study quantum gains in a lossless multiple phase interferometry model and argue that the analysis solely based on quantum Fisher information is insufficient. Contrary to previous results, we demonstrate that the optimal simultaneous estimation scheme only provides a constant factor improvement compared to schemes where each phase is estimated separately.