Optimal Distributed quantum sensing using Gaussian states

TL;DR

This paper identifies the optimal Gaussian state scheme for distributed quantum sensing of phase shifts, highlighting the role of entanglement and measurement types in achieving ultimate sensitivity, especially under loss conditions.

Contribution

It demonstrates the optimality of entangled symmetric Gaussian states and analyzes measurement strategies, revealing the need for non-Gaussian measurements in lossy environments.

Findings

Entangled symmetric Gaussian states achieve ultimate sensitivity in ideal conditions.

Homodyne detection is optimal without loss, but less so with loss.

Non-Gaussian measurements are necessary for optimal sensitivity under loss.

Abstract

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaussian state. It is also demonstrated that when loss occurs, homodyne detection and other types of Gaussian measurements compete for better sensitivity, depending on the amount of loss and properties of a probe state. None of them provide the ultimate sensitivity, indicating that non-Gaussian measurements are required for optimality in lossy cases. Our general results obtained through a full-analytical investigation will offer important perspectives to the future theoretical and experimental study for quantum distributed Gaussian sensing.