Graph States as a Resource for Quantum Metrology

Nathan Shettell, Damian Markham

Published 2019-08-14Version 1

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 attain a QFI of at least of at least $n^{2-\log_n k}$, we call these states bundled graph states. We also quantify the number of $n$ qubit stabilizer states that are useful as a resource for quantum metrology. 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.