Optimal Multiparameter Metrology: The Quantum Compass Solution

• DOI: 10.48550/arxiv.2404.14194
• Publication Date: 2024-04-22
• Authors: Denis V. Vasilyev; Athreya Shankar; Raphael Kaubruegger; P. Zoller
• Keywords: Compass; Quantum Metrology

We study optimal quantum sensing of multiple physical parameters using repeated measurements. In this scenario, the Fisher information framework sets fundamental limits on performance, yet states and corresponding measurements that attain these remain to be discovered. To address this, we extend approach with a second optimality requirement for sensor provide unambiguous estimation unknown parameters. propose systematic method integrating Bayesian approaches metrology identify combination input satisfies both criteria. Specifically, frame problem as an optimization asymptotic cost function can efficiently solved numerically and, in many cases, analytically. refer resulting `quantum compass' solution, which serves direct multiparameter counterpart Greenberger-Horne-Zeilinger state-based interferometer, renowned achieving Heisenberg limit single-parameter metrology. exact compass solutions paradigmatic two three SU(2) sensor. Our metrological opens avenues variational techniques design low-depth circuits approaching performance many-repetition scenario. demonstrate by constructing simple achieve vector field 3D rotations limited set gates available trapped-ion platform. work introduces optimizes sensors practical notion optimality, keeping mind ultimate goal precisely estimate