Multiphase estimation without a reference mode

TL;DR

This paper explores multiphase quantum estimation without a shared reference mode, revealing how resource limitations and symmetries influence the optimal strategies and the number of estimable parameters.

Contribution

It generalizes multiphase estimation by removing the reference mode, analyzing the impact on parameter estimability and optimal probe state design.

Findings

Removing the reference mode limits the number of estimable parameters.

Symmetries of the parameters determine the symmetries of optimal probe states.

Provides practical insights for constructing optimal measurements in resource-constrained scenarios.

Abstract

Multiphase estimation is a paradigmatic example of a multiparameter problem. When measuring multiple phases embedded in interferometric networks, specially-tailored input quantum states achieve enhanced sensitivities compared with both single-parameter and classical estimation schemes. Significant attention has been devoted to defining the optimal strategies for the scenario in which all of the phases are evaluated with respect to a common reference mode, in terms of optimal probe states and optimal measurement operators. As well, the strategies assume unlimited external resources, which is experimentally unrealistic. Here, we optimize a generalized scenario that treats all of the phases on an equal footing and takes into account the resources provided by external references. We show that the absence of an external reference mode reduces the number of simultaneously estimatable parameters, owing to the immeasurability of global phases, and that the symmetries of the parameters being estimated dictate the symmetries of the optimal probe states. Finally, we provide insight for constructing optimal measurements in this generalized scenario. The experimental viability of this work underlies its immediate practical importance beyond fundamental physics.