# Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks

## TL;DR

This paper introduces a quantum sensor network protocol that leverages entanglement to significantly improve the precision of estimating analytic functions of multiple parameters, with proven optimality for qubits and potential applications in quantum computing.

## Contribution

It generalizes previous work to multiple parameters, demonstrating an entanglement-based protocol that achieves optimal measurement scaling for qubit sensors and proposing extensions for photonic systems.

## Key findings

- Entanglement improves estimation accuracy by a factor proportional to the number of parameters.
- The protocol is proven optimal for qubit sensors.
- Potential applications include calibration in quantum computing.

## Abstract

We generalize past work on quantum sensor networks to show that, for $d$ input parameters, entanglement can yield a factor $\mathcal O(d)$ improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.