Cavity-magnon systems are emerging as a fruitful architecture for the integration of quantum technologies and spintronic technologies, where magnons are coupled to microwave photons via the magnetic-dipole interaction. Controllable, the photon-magnon (P-M) couplings provide a powerful means of accessing and manipulating quantum states in such hybrid systems. Thus, determining the relevant P-M couplings is a fundamental task. Here we address the quantum estimation problem for the P-M coupling strength in a double-cavity-magnon system with drive and dissipation. The effects of various physical factors on the estimation precision are investigated and the underlying physical mechanisms are discussed in detail. Considering that in practical experiments it is almost infeasible to perform measurements on the global quantum state of this composite system, we identify the optimal subsystem for performing measurements and estimations. Further, we evaluate the performance of different Gaussian measurements, indicating that optimal Gaussian measurement almost saturates the ultimate theoretical bound on the estimation precision given by the quantum Fisher information.
Cavity-magnon systems are emerging as a fruitful architecture for the integration of quantum technologies and spintronic technologies, where magnons are coupled to microwave photons via the magnetic-dipole interaction. Controllable, the photon-magnon (P-M) couplings provide a powerful means of accessing and manipulating quantum states in such hybrid systems. Thus, determining the relevant P-M couplings is a fundamental task. Here we address the quantum estimation problem for the P-M coupling strength in a double-cavity-magnon system with drive and dissipation. The effects of various physical factors on the estimation precision are investigated and the underlying physical mechanisms are discussed in detail. Considering that in practical experiments it is almost infeasible to perform measurements on the global quantum state of this composite system, we identify the optimal subsystem for performing measurements and estimations. Further, we evaluate the performance of different Gaussian measurements, indicating that optimal Gaussian measurement almost saturates the ultimate theoretical bound on the estimation precision given by the quantum Fisher information.
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.
Multiparameter quantum metrology plays a fundamental role in uncovering and exploiting the distinctive features of quantum systems. In this work, we propose an effective and experimentally feasible scheme to significantly enhance the simultaneous quantum estimation of the photon magnon and magnon mechanical coupling strengths in a hybrid cavity magnon mechanical platform. Our approach relies on the assistance of a coherent feedback loop combined with the injection of a coherent driving field. We show that an appropriate tuning of the system and feedback parameters leads to a substantial reduction of the estimation errors associated with both coupling strengths. To quantify the metrological performance of the proposed scheme, we employ the quantum Cramer Rao bound (QCRB) as a fundamental benchmark for multiparameter estimation. We explicitly compute and compare the QCRBs derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) formalisms. Our results demonstrate that the RLD based QCRB is systematically lower than the SLD based bound, indicating superior estimation precision in the considered noncommutative estimation scenario. We further analyze the performance of heterodyne detection and show that, in suitable parameter regimes, the corresponding classical estimation precision closely approaches the ultimate quantum limit predicted by our scheme. Finally, we discuss the experimental feasibility of the proposed setup within currently available cavity magnon mechanical platforms. Owing to its general character, the framework developed here can be readily extended to the high precision estimation of other physical parameters in hybrid quantum systems.
Improving multiparameter quantum estimation in magnonic systems via quantum noise suppression is a well-established and critical research objective. In this work, we propose an experimentally realistic scheme to improve the precision of simultaneously estimating different parameters in a cavity-magnon system by utilizing a degenerate optical parametric amplifier (OPA). The OPA enhances the estimation precision by decreasing the most informative quantum Cramér-Rao bound, calculated employing the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD). We show that when nonlinearity is introduced into the system, quantum noise is significantly suppressed. Our results show how different physical parameters influence multiparameter estimation precision and provide a detailed discussion of the associated physical mechanisms in the steady state. Our results focus on exploring practical Gaussian measurement schemes that can be realized experimentally. Besides, we further analyze the system's dynamics, comparing both the SLD quantum Fisher information (QFI) and the classical Fisher information (CFI) for both homodyne and heterodyne detection. This approach provides a robust foundation for multiparameter quantum estimation, offering significant potential for application in hybrid magnomechanical and optomechanical systems.
In this work, we introduce an experimentally viable scheme to enhance the simultaneous estimation precision of the couplings Gmc and Gmb, with a particular focus on the performance of heterodyne detection. By comparing simultaneous and individual estimation strategies, we demonstrate that the simultaneous approach offers a notable advantage in our system. To support this, we compute the quantum Fisher information matrices (QFIMs) based on the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD). Our results show that the quantum Cramér Rao bound (QCRB) associated with the RLD is consistently lower than that of the SLD, indicating superior estimation precision. From a physical standpoint, this improvement reflects the system's enhanced capacity to encode, transfer, and extract quantum information while allowing optimal control of fundamental interactions. We show that increasing the Rabi frequency, cavity loss rate, and the average number of photons and phonons, combined with reduced mechanical damping and temperature, enhances the system's sensitivity to the coupling parameters. These mechanisms act on the available quantum resources, such as entanglement, squeezing, and state purity, leading to more precise estimations. Furthermore, our analysis reveals that under certain conditions, heterodyne detection can closely approach the ultimate precision set by the QFIM. This suggests that a measurement strategy based on heterodyne detection can offer an efficient and practical route for estimating the couplings Gmc and Gmb, paving the way for high precision hybrid quantum sensors.
Tripartite interactions play a fundamental role in the quantum information processing and quantum technology. However, it is generally difficult to realize strong tripartite coupling. We investigate the estimation of a tripartite coupling strength in a hybrid setup composed of a single nitrogen-vacancy (NV) center and a micromagnet. A time-independent parametric drive can be utilized to increase the estimation precision of the tripartite coupling strength. By calculating the quantum Fisher information (QFI), we can obtain the optimal estimation precision by measuring the eigenstate of the tripartite system. At the critical position, the QFI is divergent due to that the preparation time of the eigenstate is divergent. When the system is subjected to a dissipation, the QFI near the critical point of the driven-dissipation phase transition is analytically obtained. The direct intensity measurement is the optimal measurement near the dissipation phase transition point. In addition, we quantify the robustness of an imperfect measurement operator by the measurement noise susceptibility based on the error propagation formula. We find that the direct intensity measurement is robust enough against small measurement disturbance from a coherent drive. But it can be disturbed by the nonlinear anti-harmonic measurement noise, especially near the critical point.
Multiparameter quantum estimation has emerged as a central task in quantum metrology. In this work, we investigate multiparameter quantum estimation in a hybrid exciton--optomechanical (EOM) system. The system consists of a semiconductor quantum well embedded inside a driven optomechanical microcavity, where the excitonic, optical, and mechanical modes interact coherently through exciton--photon and radiation-pressure couplings. Using the Gaussian-state formalism, we derive the covariance matrix of the steady-state quantum fluctuations and employ both the symmetric logarithmic derivative (SLD) and right logarithmic derivative (RLD) approaches to evaluate the quantum Fisher information matrix associated with the simultaneous estimation of the exciton--photon coupling strength g and the excitonic decay rate kx. We analyze the corresponding quantum Cramér--Rao bounds and determine the most informative precision limit governing the attainable estimation accuracy. The influence of several experimentally relevant parameters, including temperature, driving power, optomechanical coupling strength, and dissipation rates, is investigated in detail. Our results show that strong hybrid interactions and low-temperature regimes significantly enhance the estimation precision, whereas thermal fluctuations and dissipation processes deteriorate the metrological performance. Furthermore, we compare the ultimate quantum limits with experimentally feasible Gaussian measurement strategies based on homodyne and heterodyne detection. We show that heterodyne detection provides better estimation performance than homodyne schemes and can approach the optimal quantum precision limit in suitable parameter regimes.