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:1503.05697 · Physical Review A

Maximal quantum Fisher information for general su(2) parametrization processes

Xiao-Xing Jing, Jing Liu, Heng-Na Xiong, Xiaoguang Wang

Published Jul 10, 2015• 35 citations
arXivHTMLPDF

Abstract

Quantum Fisher information is a key concept in the field of quantum metrology, which aims to enhance the accuracy of parameter estimation by using quantum resources. In this paper, utilizing a representation of quantum Fisher information for a general unitary parametrization process, we study unitary parametrization processes governed by su(2) dynamics. We obtain the analytical expression for the Hermitian operator of the parametrization and the maximal quantum Fisher information. We find that the maximal quantum Fisher information over the parameter space consists of two parts; one is quadratic in time and the other oscillates with time. We apply our result to the estimation of a magnetic field and obtained the maximal quantum Fisher information. We further discuss a driving field with a time-dependent Hamiltonian and find that the maximal quantum Fisher information of the driving frequency attains the optimum when it is in resonance with the atomic frequency.

DOI
10.1103/physreva.92.012312

Related papers

Quantum metrology with unitary parametrization processes

Jing Liu, Xiao-Xing Jing, Xiaoguang Wang

Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. Furthermore, H can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.

arXiv:1409.4057•Scientific Reports•Feb 24, 2015•95 citations

Quantum metrology for a general Hamiltonian parameter

Shengshi Pang, Todd A. Brun

Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-$\frac{1}{2}$ particle and compare the results for estimating the amplitude and the direction of the magnetic field.

arXiv:1407.6091•Physical Review A•Aug 25, 2014•175 citations

Quantum Fisher information for unitary parametrization processes governed by arbitrary Lie algebras

Hongbin Liang, Fei Yao, Xiao-Xing Jing +2 more

Abstract Quantum Fisher information (QFI) is a key concept of quantum metrology, which is widely used in quantum parameter estimation. We introduce a general approach to analytically get the QFI of pure states for unitary parametrization processes governed by arbitrary finite dimensional Lie algebras. We show the universality of this approach by comparing the result of algebra with the previous work and applying it to and algebras. For case, there are some interesting findings. The phase of the initial coherent state has an optimal value for maximum QFI, and the QFI can vanish and revive during the time evolution.

Journal of Physics A Mathematical and Theoretical•Jun 8, 2018•1 citation

Quantum Fisher information power of quantum evolutions

Jun‐Long Zhao, Yanhui Zhou, Dong‐Xu Chen +5 more

Abstract Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV = 1.

Journal of Physics A Mathematical and Theoretical•Jun 6, 2024•0 citations

Relations between quantum metrology and criticality in general su(1,1) systems

Rui Zhang, Wenkui Ding, Zhucheng Zhang +3 more

There is a prevalent effort to achieve quantum-enhanced metrology using criticality. However, the extent to which estimation precision is enhanced through criticality still needs further exploration under the constraint of finite time resources. We clarify relations between quantum metrology and criticality through a unitary parametrization process with a Hamiltonian governed by $\text{su}(1,1)$ Lie algebra. We demonstrate that the determination of the generator in the parametrization can be treated as an extended brachistochrone problem. Furthermore, the dynamic quantum Fisher information about the parameter exhibits a power-law dependence on the evolution time as the system approaches its critical point. By investigating the dynamic sensing proposals of three quantum critical systems, we show that the asymptotic behavior of sensitivity is consistent with our predictions. Our theory provides a deep understanding of the interplay of quantum metrology and criticality, providing insights into the underlying connections that involve both quantum phenomena and classical problems.

arXiv:2303.10655•Physical Review A•Jul 2, 2024•7 citations

Quantum metrology with time-dependent Hamiltonians

Shengshi Pang, Andrew N. Jordan

Quantum metrology has been intensively studied for a wide range of systems with static Hamiltonians. For systems with time-varying Hamiltonians, however, significant difficulty emerges, due to no explicit solution is available for the dynamics in general. This results in a lack of knowledge about quantum metrology for these more complex systems so far. In this paper, we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal solution to Fisher information, and show that proper Hamiltonian control gives an advantage in maximizing the Fisher information. We derive the optimal Hamiltonian control, and with a minimal example of a qubit in a rotating magnetic field, we find a surprising result that with the assistance of Hamiltonian control, the fundamental limit of time scaling $T^{2}$ for Fisher information can be violated with time-dependent Hamiltonians, which reaches $T^{4}$ in estimating the rotation frequency of the field. We further consider level crossings in the parametric derivatives of the Hamiltonians, and point out that additional Hamiltonian control is necessary for that case.

•Jun 7, 2016•2 citations
Quantum Fisher information is a key concept in the field of quantum metrology, which aims to enhance the accuracy of parameter estimation by using quantum resources. In this paper, utilizing a representation of quantum Fisher information for a general unitary parametrization process, we study unitary parametrization processes governed by su(2) dynamics. We obtain the analytical expression for the Hermitian operator of the parametrization and the maximal quantum Fisher information. We find that the maximal quantum Fisher information over the parameter space consists of two parts; one is quadratic in time and the other oscillates with time. We apply our result to the estimation of a magnetic field and obtained the maximal quantum Fisher information. We further discuss a driving field with a time-dependent Hamiltonian and find that the maximal quantum Fisher information of the driving frequency attains the optimum when it is in resonance with the atomic frequency.
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. Furthermore, H can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-12\frac{1}{2}21​ particle and compare the results for estimating the amplitude and the direction of the magnetic field.
Abstract Quantum Fisher information (QFI) is a key concept of quantum metrology, which is widely used in quantum parameter estimation. We introduce a general approach to analytically get the QFI of pure states for unitary parametrization processes governed by arbitrary finite dimensional Lie algebras. We show the universality of this approach by comparing the result of algebra with the previous work and applying it to and algebras. For case, there are some interesting findings. The phase of the initial coherent state has an optimal value for maximum QFI, and the QFI can vanish and revive during the time evolution.
Abstract Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV = 1.
There is a prevalent effort to achieve quantum-enhanced metrology using criticality. However, the extent to which estimation precision is enhanced through criticality still needs further exploration under the constraint of finite time resources. We clarify relations between quantum metrology and criticality through a unitary parametrization process with a Hamiltonian governed by su(1,1)\text{su}(1,1)su(1,1) Lie algebra. We demonstrate that the determination of the generator in the parametrization can be treated as an extended brachistochrone problem. Furthermore, the dynamic quantum Fisher information about the parameter exhibits a power-law dependence on the evolution time as the system approaches its critical point. By investigating the dynamic sensing proposals of three quantum critical systems, we show that the asymptotic behavior of sensitivity is consistent with our predictions. Our theory provides a deep understanding of the interplay of quantum metrology and criticality, providing insights into the underlying connections that involve both quantum phenomena and classical problems.
Quantum metrology has been intensively studied for a wide range of systems with static Hamiltonians. For systems with time-varying Hamiltonians, however, significant difficulty emerges, due to no explicit solution is available for the dynamics in general. This results in a lack of knowledge about quantum metrology for these more complex systems so far. In this paper, we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal solution to Fisher information, and show that proper Hamiltonian control gives an advantage in maximizing the Fisher information. We derive the optimal Hamiltonian control, and with a minimal example of a qubit in a rotating magnetic field, we find a surprising result that with the assistance of Hamiltonian control, the fundamental limit of time scaling T2T^{2}T2 for Fisher information can be violated with time-dependent Hamiltonians, which reaches T4T^{4}T4 in estimating the rotation frequency of the field. We further consider level crossings in the parametric derivatives of the Hamiltonians, and point out that additional Hamiltonian control is necessary for that case.