Local versus Global Strategies in Multi-parameter Estimation

TL;DR

This paper demonstrates that local, separable states with high number variance can achieve the same precision as entangled global strategies in multi-parameter quantum estimation, offering practical advantages.

Contribution

It shows that quantum enhancement in multi-parameter estimation does not require entanglement, emphasizing the role of number variance and advocating for local measurement strategies.

Findings

Separable states with large number variance can match entangled strategies in precision.

Local measurement strategies are more robust and easier to implement than global entangled schemes.

The results apply to quantum sensor networks and quantum imaging contexts.

Abstract

We consider the problem of estimating multiple phases using a multi-mode interferometer. In this setting we show that while global strategies with multi-mode entanglement can lead to high precision gains, the same precision enhancements can be obtained with mode-separable states and local measurements. The crucial resource for quantum enhancement is shown to be a large number variance in the probe state, which can be obtained without any entanglement between the modes. This has important practical implications because local strategies using separable states have many advantages over global schemes using multi-mode-entangled states. Such advantages include a robustness to local estimation failure, more flexibility in the distribution of resources, and comparatively easier state preparation. We obtain our results by analyzing two different schemes: the first uses a set of interferometers, which can be used as a model for a network of quantum sensors, and the second looks at measuring a number of phases relative to a reference, which is concerned primarily with quantum imaging.