# Graph States as a Resource for Quantum Metrology

## TL;DR

This paper explores the use of graph states in quantum metrology, demonstrating their robustness against noise and their potential to achieve high precision measurements.

## Contribution

It characterizes the quantum Fisher information of graph states and introduces bundled graph states that maintain quantum advantage under noise.

## Key findings

- Bundled graph states approach the Heisenberg limit.
- They retain quantum advantage after noise exposure.
- Quantifies useful stabilizer states for quantum metrology.

## Abstract

By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum advantage in realistic conditions. In this study we investigate the practicality of graph states for quantum metrology. Graph states are a natural resource for much of quantum information, and here we characterize their quantum Fisher information (QFI) for an arbitrary graph state. We then construct families of graph states which approximately achieves the Heisenberg limit, we call these states bundled graph states. We demonstrate that bundled graph states maintain a quantum advantage after being subjected to iid dephasing or finite erasures. This shows that these graph states are good resources for robust quantum metrology. We also quantify the number of n qubit stabilizer states that are useful as a resource for quantum metrology.