A protocol for global multiphase estimation

TL;DR

This paper introduces a global multiphase estimation protocol based on Holevo's theory, demonstrating its performance and quantum advantage in estimating multiple phases simultaneously without prior knowledge.

Contribution

It develops a comprehensive multiphase estimation protocol extending known strategies and evaluates its quantum advantage and ultimate precision bounds.

Findings

The protocol encompasses known optimal strategies in single-phase estimation.

It extends to simultaneous estimation of two phases and evaluates performance.

Shows only a constant quantum advantage in multiphase estimation over independent single-phase methods.

Abstract

Global estimation strategies allow to extract information on a phase or a set of phases without any prior knowledge, which is, instead, required for local estimation strategies. We devise a global multiphase protocol based on Holevo's estimation theory and apply it to the case of digital estimation, i.e. we estimate the phases in terms of the mutual information between them and the corresponding estimators. In the single-phase scenario, the protocol encompasses two specific known optimal strategies. We extend them to the simultaneous estimation of two phases and evaluate their performance. Then, we retrieve the ultimate digital bound on precision when a generic number of phases is simultaneously estimated. We show that in the multiphase strategy there is only a constant quantum advantage with respect to a sequence of independent single-phase estimations. This extends a recent similar result, which settled a controversy on the search for the multiphase enhancement.