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

Results in Physics

Bayesian quantum parameter estimation with Gaussian states and homodyne measurements in a dissipative environment

Jie Tang, Huicun Yu, Ying Liu, Zhi-Feng Deng, Jiahao Li, Yuexiang Cao, Jiahua Wei, Lei Shi

Published Mar 21, 2023• 3 citations
Publisher

Abstract

The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of quantum metrology. Therefore, it is significant to effectively analyze the evolution of quantum systems under dissipative environments and quantitatively estimate the parameters given a certain probe. Here, we propose a continuous-variable (CV) quantum metrology scheme within the Bayesian paradigm to estimate phase shift, loss coefficient and temperature of a dissipative environment. Through simulation analysis, we investigate the achievable precision of Bayesian quantum parameter estimation with Gaussian states and homodyne measurements, and the influence of different parameters on the estimation process. More interestingly, the scheme can be applied in more practical scenarios where not enough measurements are obtained and the frequentist analysis is not well defined.

DOI
10.1016/j.rinp.2023.106383

Related papers

Bayesian parameter estimation using Gaussian states and measurements

Simon Morelli, Ayaka Usui, Elizabeth Agudelo +1 more

Abstract Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

arXiv:2009.03709•Quantum Science and Technology•Jan 4, 2021•35 citations

Bayesian parameter estimation using Gaussian states and measurements

Simon Morelli, Ayaka Usui, Elizabeth Agudelo +1 more

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramer-Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

•Mar 5, 2021•25 citations

Quantum metrology using Gaussian states and efficient Bayesian error certification

오창훈

Precise measurement of physical quantities plays a crucial role in the development of science and technology.The main purpose of the dissertation is two-fold: to investigate the ultimate precision for estimation of physical quantities using Gaussian states and to propose an efficient method for certification of Bayesian error region in general quantum parameter estimation.In the first part, we begin with analyzing sensitivity for estimating a phase difference in an optical interferometer.Optical interferometry is widely used in science and industry for measuring small displacements.Recently, a large-scale optical interferometer socalled the Laser interferometer Gravitational-Wave Observatory (LIGO) has succeeded in detecting a gravitational wave, the signal of which is extremely small.On the other hand, it has been shown that a non-classical feature of quantum states can improve the sensitivity of estimation, such as in optical interferometer, including the LIGO.From a practical point of view, we inspect the practically achievable precision using non-classical Gaussian states in Mach-Zehnder interferometer with feasible measurements and realistic photon loss.We then investigate the precision of single-mode phase estimation using Gaussian measurement, which can be realized by using homodyne detection, and i show that non-Gaussian measurement is necessary to utilize the power of Gaussian input probes optimally.Finally, we find the optimal measurement for general Gaussian quantum metrology and identify three distinct optimal measurements corresponding to different circumstances.In the second part, we study the Bayesian error region, which is a crucial concept for a general estimation process.When estimating a physical quantity, one has to supply the error interval (single-parameter) or error region (multi-parameter) as well as the estimate.However, it has been shown that as the dimension of quantum systems of interest grows, it becomes intractable to calculate the size and credibility of Bayesian error regions.As an alternative, we derive an analytical expression for the properties, the size and credibility, of Bayesian error regions, in an asymptotic regime.We then propose an efficient numerical method to calculate them for high-dimensional quantum systems even in a non-asymptotic regime.

•Nov 23, 2020•0 citations

Gaussian quantum metrology in a dissipative environment

Wei Wu, Jun‐Hong An

Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the long-encoding-time regime due to the Born-Markovian approximate decoherence, which is called the no-go theorem of noisy quantum metrology. Here we propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as the quantum probe. It achieves the precision of a sub-Heisenberg limit in the ideal case. However, the Markovian decoherence causes the metrological error contributed by the center-of-mass mode of the probe to be divergent. A mechanism to remove this ostensible no-go theorem is found in the non-Markovian dynamics. Our result gives an efficient way to realize high-precision quantum metrology in practical continuous-variable systems.

arXiv:2107.13161•Physical Review A•Oct 28, 2021•11 citations

Quantum parameter estimation in a dissipative environment

Wei Wu, Chuan Shi

We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.

arXiv:2110.07825•Physical Review A•Sep 8, 2020•34 citations

Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

Changhun Oh, Changhyoup Lee, Carsten Rockstuhl +4 more

Abstract The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators $$\hat X\hat P + \hat P\hat X$$ X ̂ P ̂ + P ̂ X ̂ , i.e., a non-Gaussian measurement, is required to be fully optimal.

arXiv:1805.08495•npj Quantum Information•Jan 28, 2019•81 citations
The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of quantum metrology. Therefore, it is significant to effectively analyze the evolution of quantum systems under dissipative environments and quantitatively estimate the parameters given a certain probe. Here, we propose a continuous-variable (CV) quantum metrology scheme within the Bayesian paradigm to estimate phase shift, loss coefficient and temperature of a dissipative environment. Through simulation analysis, we investigate the achievable precision of Bayesian quantum parameter estimation with Gaussian states and homodyne measurements, and the influence of different parameters on the estimation process. More interestingly, the scheme can be applied in more practical scenarios where not enough measurements are obtained and the frequentist analysis is not well defined.
Abstract Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramer-Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.
Precise measurement of physical quantities plays a crucial role in the development of science and technology.The main purpose of the dissertation is two-fold: to investigate the ultimate precision for estimation of physical quantities using Gaussian states and to propose an efficient method for certification of Bayesian error region in general quantum parameter estimation.In the first part, we begin with analyzing sensitivity for estimating a phase difference in an optical interferometer.Optical interferometry is widely used in science and industry for measuring small displacements.Recently, a large-scale optical interferometer socalled the Laser interferometer Gravitational-Wave Observatory (LIGO) has succeeded in detecting a gravitational wave, the signal of which is extremely small.On the other hand, it has been shown that a non-classical feature of quantum states can improve the sensitivity of estimation, such as in optical interferometer, including the LIGO.From a practical point of view, we inspect the practically achievable precision using non-classical Gaussian states in Mach-Zehnder interferometer with feasible measurements and realistic photon loss.We then investigate the precision of single-mode phase estimation using Gaussian measurement, which can be realized by using homodyne detection, and i show that non-Gaussian measurement is necessary to utilize the power of Gaussian input probes optimally.Finally, we find the optimal measurement for general Gaussian quantum metrology and identify three distinct optimal measurements corresponding to different circumstances.In the second part, we study the Bayesian error region, which is a crucial concept for a general estimation process.When estimating a physical quantity, one has to supply the error interval (single-parameter) or error region (multi-parameter) as well as the estimate.However, it has been shown that as the dimension of quantum systems of interest grows, it becomes intractable to calculate the size and credibility of Bayesian error regions.As an alternative, we derive an analytical expression for the properties, the size and credibility, of Bayesian error regions, in an asymptotic regime.We then propose an efficient numerical method to calculate them for high-dimensional quantum systems even in a non-asymptotic regime.
Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the long-encoding-time regime due to the Born-Markovian approximate decoherence, which is called the no-go theorem of noisy quantum metrology. Here we propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as the quantum probe. It achieves the precision of a sub-Heisenberg limit in the ideal case. However, the Markovian decoherence causes the metrological error contributed by the center-of-mass mode of the probe to be divergent. A mechanism to remove this ostensible no-go theorem is found in the non-Markovian dynamics. Our result gives an efficient way to realize high-precision quantum metrology in practical continuous-variable systems.
We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.
Abstract The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators X^P^+P^X^\hat X\hat P + \hat P\hat XX^P^+P^X^ X ̂ P ̂ + P ̂ X ̂ , i.e., a non-Gaussian measurement, is required to be fully optimal.