Enhancement of quantum estimation in cavity magnonics

Abstract Quantum metrology enables measurement sensitivities beyond classical limits by exploiting quantum resources. Among promising platforms, hybrid cavity–magnon systems—where microwave photons interact with collective spin excitations in magnetic materials—offer a versatile testbed for emerging quantum technologies. However, their performance hinges on precise knowledge of the cavity–magnon coupling strength. Here, we propose an experimentally feasible scheme to enhance the quantum estimation of this parameter by leveraging coherent feedback and parametric amplification. Using the Heisenberg–Langevin formalism, we linearize the system dynamics and compute both quantum (QFI) and classical Fisher information. Our analysis shows that optimal detuning, strong driving, and cryogenic temperatures below 0.1 K significantly improve estimation precision, while magnon dissipation and thermal noise degrade the QFI. Parametric amplification enhances precision when the gain and phase are optimally tuned, and coherent feedback yields even greater sensitivity at tailored phase shifts and reflectivities. Notably, their combination achieves the lowest estimation error and the highest robustness against thermal noise. Finally, we identify the cavity mode as the optimal probe, with homodyne detection nearly saturating the quantum limit under ideal conditions. These findings establish a robust pathway for high-precision, noise-resilient cavity–magnon coupling estimation.