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:1208.0104 · Physical Review A

Hierarchy of measurement-induced Fisher information for composite states

Xiao-Ming Lu, Shunlong Luo, C. H. Oh

Published Aug 31, 2012• 34 citations
arXivHTMLPDF

Abstract

Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this paper, we exploit the classical Fisher information induced by quantum measurements and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc.

DOI
10.1103/physreva.86.022342

Related papers

Quantum fisher information transfer and distribution in a hierarchical environment

You-neng Guo, Qinglong Tian

How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.

Results in Physics•Sep 1, 2025•0 citations

Distribution of quantum Fisher information in spin channel

Hongting Song

Towards the statistical distinguishability about parameters encoded in the bipartite quantum state, we mainly investigate the distribution and transformation of quantum Fisher information over composite systems in spin channel. The relationship between the global quantum Fisher information and the sum of the locally accessible quantum Fisher information are studied, which can be subadditivity, additivity, or superadditivity. The transfer among them under the unitary operation is illustrated. We find that the quantum Fisher information can not only flow between the reduced systems, but also between the different types of distribution.

Chinese Control Conference (CCC)•Jul 1, 2020•0 citations

Quantum Correlations and Local Quantum Fisher Information

Sunho Kim, Longsuo Li, Junde Wu

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in \cite{Lu}, we show that the presence of a quantum correlations can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord in pure state.

•Nov 7, 2017•0 citations

Enhancing Quantum Metrology with High-order Fisher Information and Experiments

Xin-Zhu Liu, Jun-Li Jiang, Yan-Han Yang +4 more

Fisher information plays a central role in statistics and quantum metrology, providing the basis for the celebrated Cramér-Rao bound. In this work, we introduce a new information measure based on higher-order Fisher information and show that it naturally leads to a generalized uncertainty relation for parameter estimation, which can be regarded as an extension of the Cramér-Rao bound. As an application, we analyze the case of quantum phase estimation with a single qubit and compare our theoretical bounds with the well-known established hierarchical bounds. Finally, we experimentally validate the proposed framework using a photonic platform.

quant-pharXiv:2606.27633•Jun 29, 2026•0 citations

Information Geometry under Hierarchical Quantum Measurement

Hongzhen Chen, Yu Chen, Haidong Yuan

In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of quantum and classical informations. Here we analyze the difference in terms of the Fisher information metric and present a framework that can provide analytical bounds on the discrepancy under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multiparameter quantum metrology, which leads to characterizations of the trade-off among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.

arXiv:2206.13095•Physical Review Letters•Jun 24, 2022•24 citations

Quantum non-Markovianity based on the Fisher-information matrix

Hongting Song, Shunlong Luo, Yan Hong

With the development of quantum-information theory, there has been a flurry of investigations of quantum non-Markovian dynamics, and several significant measures for such dynamics have been proposed from various perspectives, such as the breakdown of dynamical divisibility, increase in the distinguishability between quantum states, increase in correlations between the system and an arbitrary ancillary, and so on. Motivated by the idea of exploiting the information content of parameters encoded in initial states, we propose a conceptually simple and physically intuitive characterization for non-Markovianity with the help of a quantum-Fisher-information matrix. The basic features are illustrated through several examples, and relations with other approaches are elucidated. A hierarchial aspect of quantum non-Markovianity is revealed.

Physical Review A•Apr 10, 2015•65 citations
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this paper, we exploit the classical Fisher information induced by quantum measurements and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc.
How quantum information encoded into a quantum state is lost, or transferred when an interest quantum system is coupled to its environment, is a fundamental issue in quantum information processing. In this paper, we systematically investigate the dynamics of Quantum Fisher Information (QFI) transfer and QFI flow in a hybrid quantum system composed of a three-level atom located in a cavity interacting with its own reservoir. Our analysis demonstrates that the phase (amplitude)-encoded QFI, initially localized in the atomic subsystem is completely transferred into the reservoir subsystem, as the cavity is as a bridge connecting atom to reservoir. Extending our investigation to two individual subsystems case where the QFI transfer and distribution are studied. Crucially, the relationship between the sum of the locally accessible QFI and the global QFI exhibits subadditivity, additivity, or superadditivity strongly depending on the initial entanglement configuration of the atomic states. Furthermore, the amount of information flowing from the environment (cavity plus reservoir) back into the system is also explicitly revealed by QFI flow which provides an indicator to characterizes the non-Markovianity of the open systems’ dynamics.
Towards the statistical distinguishability about parameters encoded in the bipartite quantum state, we mainly investigate the distribution and transformation of quantum Fisher information over composite systems in spin channel. The relationship between the global quantum Fisher information and the sum of the locally accessible quantum Fisher information are studied, which can be subadditivity, additivity, or superadditivity. The transfer among them under the unitary operation is illustrated. We find that the quantum Fisher information can not only flow between the reduced systems, but also between the different types of distribution.
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in \cite{Lu}, we show that the presence of a quantum correlations can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord in pure state.
Fisher information plays a central role in statistics and quantum metrology, providing the basis for the celebrated Cramér-Rao bound. In this work, we introduce a new information measure based on higher-order Fisher information and show that it naturally leads to a generalized uncertainty relation for parameter estimation, which can be regarded as an extension of the Cramér-Rao bound. As an application, we analyze the case of quantum phase estimation with a single qubit and compare our theoretical bounds with the well-known established hierarchical bounds. Finally, we experimentally validate the proposed framework using a photonic platform.
In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of quantum and classical informations. Here we analyze the difference in terms of the Fisher information metric and present a framework that can provide analytical bounds on the discrepancy under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multiparameter quantum metrology, which leads to characterizations of the trade-off among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.
With the development of quantum-information theory, there has been a flurry of investigations of quantum non-Markovian dynamics, and several significant measures for such dynamics have been proposed from various perspectives, such as the breakdown of dynamical divisibility, increase in the distinguishability between quantum states, increase in correlations between the system and an arbitrary ancillary, and so on. Motivated by the idea of exploiting the information content of parameters encoded in initial states, we propose a conceptually simple and physically intuitive characterization for non-Markovianity with the help of a quantum-Fisher-information matrix. The basic features are illustrated through several examples, and relations with other approaches are elucidated. A hierarchial aspect of quantum non-Markovianity is revealed.