Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2002.03249 · Physical Review A

Fisher-information-based estimation of optomechanical coupling strengths

Claudio Sanavio, József Zsolt Bernád, André Xuereb

Published Jul 9, 2020• 20 citations
arXivHTMLPDF

Abstract

The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.

DOI
10.1103/physreva.102.013508

Related papers

Optomechanical systems with linear and quadratic position couplings: Dynamics and optimal estimation

Yaqing Xy Wang, Claudio Sanavio, József Zsolt Bernád

We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.

arXiv:2507.00187•Physical Review A•Jan 16, 2026•1 citation

Estimation of disorders in the rest positions of two membranes in optomechanical systems

Claudio Sanavio, József Zsolt Bernád, André Xuereb

The formalism of quantum estimation theory is applied to estimate the disorders in the positions of two membranes positioned in a driven optical cavity. We consider the coupled-cavity and transmissive-regime models to obtain effective descriptions of this system for different reflectivity values of the membranes. Our models consist also of high-temperature Brownian motions of the membranes, losses of the cavity fields, the input-output formalism, and a balanced homodyne photodetection of the cavity output field. In this two-parameter estimation scenario, we compare the classical and quantum Fisher information matrices and evaluate the accuracies of the estimations. We show that models offer very different estimation strategies and the temperature does not have a detrimental effect on the estimation accuracies but makes it more difficult to attain the quantum optimal limit. Our analysis, based on recent experimental parameter values, also reveals that the best estimation strategies with unit efficient detectors are measurements of the quadratures of the output field.

arXiv:2111.09583•Physical Review A•Mar 10, 2022•3 citations

Optimal estimation of the optomechanical coupling strength

József Zsolt Bernád, Claudio Sanavio, André Xuereb

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely results in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times on the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

arXiv:1712.09712•Physical Review A•Jun 12, 2018•22 citations

Achieving optimal multiparameter quantum estimation in optomechanics

A. Naimy, Abdallah Slaoui, Abderrahim Lakhfif +2 more

Accurate simultaneous estimation of temperature and effective detuning is crucial for understanding, controlling, and optimizing optomechanical systems. Temperature characterizes the thermal state and mechanical properties, while detuning governs the light-motion interaction, influencing stability and enabling diverse quantum applications. Precise estimates of these parameters are therefore essential to exploit the full potential of such systems in high-precision metrology and the exploration of macroscopic quantum phenomena. In this work we investigate the simultaneous estimation of the effective detuning Δ and the mirror temperature T in a Fabry-Pérot cavity system, with a particular focus on the performance of heterodyne detection. Using analytical expressions for the quantum Fisher information matrices (QFIM) derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD), we demonstrate that the quantum Cramér-Rao bound associated with the RLD is consistently lower than that based on the SLD, highlighting superior estimation precision. This gap between the SLD- and RLD-based bounds becomes especially pronounced in certain physical regimes, emphasizing the relevance of choosing the appropriate formalism in noncommutative estimation scenarios. From a physical perspective, the improved estimation performance stems from the fact that temperature directly influences thermal fluctuations in the mechanical mode, while the effective detuning modulates the strength of the optomechanical interaction, shaping the information exchange between optical and mechanical subsystems. We showed that using higher optical power, greater cavity decay rate, increased photon and phonon numbers, and reduced coupling strength improves the precision of both parameter estimates. These physical mechanisms affect the available quantum resources in the system—such as squeezing, entanglement, and state purity—which in turn determine the ultimate sensitivity achievable. Furthermore, our analysis shows that heterodyne detection can, under certain conditions, approach the ultimate precision set by the QFIM. Thus, a measurement strategy based on heterodyne detection could enable the efficient estimation of temperature, achieving performance close to that of ideal quantum-limited strategies.

Physical Review A•Oct 17, 2025•6 citations

Controlling multiparameter quantum estimation in exciton-optomechanics system

Hamza Harraf, Mohamed Amazioug, Rachid Ahl Laamara

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 $k_x$. 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.

quant-pharXiv:2606.08949•Jun 9, 2026•0 citations

Optimal estimation of optomechanical couplings

József Zsolt Bernád, Claudio Sanavio, André Xuereb

We apply the formalism of quantum estimation theory to obtain information about the value of \nthe optomechanical coupling in the simplest model of two harmonic oscillators. In particular, we \ndiscuss the minimum mean-square error estimator and a quantum Cram er-Rao inequality for the \nestimation and accuracy of the coupling's value. Our estimation strategy reveals some cases, where \nquantum statistical inference is inconclusive and only prior expectations on the coupling strength \nare reassured. We show that this situations involve also the highest expected information losses. It \nis demonstrated that interaction times in the order of one time period of mechanical oscillations are \nthe most suitable for this type of estimation scenario. We also compare situations involving di erent \ninitial photon and phonon excitations.

•Dec 27, 2017•0 citations
The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.
The formalism of quantum estimation theory is applied to estimate the disorders in the positions of two membranes positioned in a driven optical cavity. We consider the coupled-cavity and transmissive-regime models to obtain effective descriptions of this system for different reflectivity values of the membranes. Our models consist also of high-temperature Brownian motions of the membranes, losses of the cavity fields, the input-output formalism, and a balanced homodyne photodetection of the cavity output field. In this two-parameter estimation scenario, we compare the classical and quantum Fisher information matrices and evaluate the accuracies of the estimations. We show that models offer very different estimation strategies and the temperature does not have a detrimental effect on the estimation accuracies but makes it more difficult to attain the quantum optimal limit. Our analysis, based on recent experimental parameter values, also reveals that the best estimation strategies with unit efficient detectors are measurements of the quadratures of the output field.
We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely results in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times on the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.
Accurate simultaneous estimation of temperature and effective detuning is crucial for understanding, controlling, and optimizing optomechanical systems. Temperature characterizes the thermal state and mechanical properties, while detuning governs the light-motion interaction, influencing stability and enabling diverse quantum applications. Precise estimates of these parameters are therefore essential to exploit the full potential of such systems in high-precision metrology and the exploration of macroscopic quantum phenomena. In this work we investigate the simultaneous estimation of the effective detuning Δ and the mirror temperature T in a Fabry-Pérot cavity system, with a particular focus on the performance of heterodyne detection. Using analytical expressions for the quantum Fisher information matrices (QFIM) derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD), we demonstrate that the quantum Cramér-Rao bound associated with the RLD is consistently lower than that based on the SLD, highlighting superior estimation precision. This gap between the SLD- and RLD-based bounds becomes especially pronounced in certain physical regimes, emphasizing the relevance of choosing the appropriate formalism in noncommutative estimation scenarios. From a physical perspective, the improved estimation performance stems from the fact that temperature directly influences thermal fluctuations in the mechanical mode, while the effective detuning modulates the strength of the optomechanical interaction, shaping the information exchange between optical and mechanical subsystems. We showed that using higher optical power, greater cavity decay rate, increased photon and phonon numbers, and reduced coupling strength improves the precision of both parameter estimates. These physical mechanisms affect the available quantum resources in the system—such as squeezing, entanglement, and state purity—which in turn determine the ultimate sensitivity achievable. Furthermore, our analysis shows that heterodyne detection can, under certain conditions, approach the ultimate precision set by the QFIM. Thus, a measurement strategy based on heterodyne detection could enable the efficient estimation of temperature, achieving performance close to that of ideal quantum-limited strategies.
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 ggg and the excitonic decay rate kxk_xkx​. 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.
We apply the formalism of quantum estimation theory to obtain information about the value of \nthe optomechanical coupling in the simplest model of two harmonic oscillators. In particular, we \ndiscuss the minimum mean-square error estimator and a quantum Cram er-Rao inequality for the \nestimation and accuracy of the coupling's value. Our estimation strategy reveals some cases, where \nquantum statistical inference is inconclusive and only prior expectations on the coupling strength \nare reassured. We show that this situations involve also the highest expected information losses. It \nis demonstrated that interaction times in the order of one time period of mechanical oscillations are \nthe most suitable for this type of estimation scenario. We also compare situations involving di erent \ninitial photon and phonon excitations.