Protocols for estimating multiple functions with quantum sensor networks: geometry and performance

TL;DR

This paper develops a new optimized sequential protocol for estimating multiple functions in quantum sensor networks, outperforming existing methods especially with many sensors, and emphasizes the geometric role of coefficient vectors in measurement accuracy.

Contribution

It introduces a new optimized sequential measurement protocol for multiple function estimation in quantum sensor networks, generalizing previous bounds and demonstrating improved performance.

Findings

Sequential protocol outperforms other strategies with many sensors.

Protocol is explicitly implementable and versatile for various applications.

Performance depends on the geometric properties of coefficient vectors.

Abstract

We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.