Distributed quantum phase sensing for arbitrary positive and negative weights

TL;DR

This paper introduces an optimal distributed quantum phase sensing scheme using Gaussian states that can handle arbitrary positive and negative weights, achieving enhanced estimation precision through entanglement management.

Contribution

It proposes a novel quantum sensing scheme tailored for arbitrary weight distributions, optimizing entanglement use and measurement strategies for improved precision.

Findings

Optimal scheme derived and shown achievable with squeezed states and homodyne detection.

Entanglement is used only among modes with positive weights, while modes with negative weights are separated.

Deeper analysis provided for the two-mode case, comparing Gaussian and non-Gaussian probes.

Abstract

Estimation of a global parameter defined as a weighted linear combination of unknown multiple parameters can be enhanced by using quantum resources. Advantageous quantum strategies may vary depending on the weight distribution, requiring the study of optimal schemes achieving a maximal quantum advantage for a given sensing scenarios. In this work, we propose an optimal distributed quantum phase sensing scheme using Gaussian states with zero displacement for an arbitrary distribution of the weights with positive and negative signs. The estimation precision of the optimal scheme is derived, and shown to be achievable by using squeezed states injected into linear beam-splitter networks and performing homodyne detection on them in the absence of loss. Interestingly, the optimal scheme exploits entanglement of Gaussian states only among the modes assigned with equal signs of the weights, but separates the modes with opposite weight signs. We also provide a deeper understanding of our finding by focusing on the two-mode case, in comparison with the cases using non-Gaussian probe states. We expect this work to motivate further studies on quantum-enhanced distributed sensing schemes considering various types of physical parameters with an arbitrary weight distribution.