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

Journal of Physics A Mathematical and Theoretical

Quantum covariance via quantum information

Xia-Yun Gui, Yi C. Huang

Published Apr 6, 2023• 1 citation
Publisher

Abstract

Abstract For a quantum state and a set of observables, S. Luo found a matrix inequality linking the quantum covariance and the quantum Fisher information defined via the symmetric logarithmic derivatives. In this paper, we provide the corresponding matrix inequality based on the Wigner–Yanase skew information.
DOI
10.1088/1751-8121/accb1f

Related papers

Generalized Wigner-Yanase skew information and generalized fisher information

Kenjiro Yanagi, Shigeru Furuichi, Ken Kuriyama

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cramer-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.

International Symposium on Information Theory and its Applications•Dec 1, 2008•0 citations

Wigner-Yanase skew information vs. quantum Fisher information

Shunlong Luo

Among concepts describing the information contents of quantum mechanical density operators, both the Wigner-Yanase skew information and the quantum Fisher information defined via symmetric logarithmic derivatives are natural generalizations of the classical Fisher information. We will establish a relationship between these two fundamental quantities and show that they are comparable.

Proceedings of the American Mathematical Society•Jul 7, 2003•201 citations

Inequalities for quantum Fisher information

Paolo Gibilisco, Daniele Imparato, Tommaso Isola

In 2003 Luo proved an inequality relating the Wigner-Yanase information and the $SLD$-information. In this paper we prove that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.

arXiv:math-ph/0702058•Feb 16, 2007•0 citations

Logarithm Versus Square Root:Comparing Quantum Fisher Information

Shun Luo

In classical statistics,the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities.In quantum theory,this uniqueness breaks down,and there are many natural quantum analogues of the Fisher information,among which two particular versions distinguish themselves by their intuitive and informational significance:The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement,and is defined via the square root of the density operator. The second arises from Helstrom's study of quantum detection in 1967,and is defined via the symmetric logarithmic derivative.The aim of this paper is to compare these two versions of quantum Fisher information,and to establish two informational inequalities relating them.

理论物理通讯：英文版•Jan 1, 2007•0 citations

Generalized Wigner-Yanase skew information and generalized Fisher information

研二郎 柳, Shigeru Furuichi, 憲 栗山

International Symposium on Information Theory and its Applications(ISITA2008), Auckland, New Zealand, 7-10, December, 2008 -- (Abstract)We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cram´er-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.

•Dec 1, 2008•0 citations

Logarithm Versus Square Root: Comparing Quantum Fisher Information

Luo Shun-Long

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance: The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom's study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper is to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.

Communications in Theoretical Physics•Apr 1, 2007•12 citations
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cramer-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.
In 2003 Luo proved an inequality relating the Wigner-Yanase information and the SLDSLDSLD-information. In this paper we prove that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality is a consequence of the Kubo-Ando inequality that states that any matrix mean is bigger than the harmonic mean and smaller than the arithmetic mean.
In classical statistics,the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities.In quantum theory,this uniqueness breaks down,and there are many natural quantum analogues of the Fisher information,among which two particular versions distinguish themselves by their intuitive and informational significance:The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement,and is defined via the square root of the density operator. The second arises from Helstrom's study of quantum detection in 1967,and is defined via the symmetric logarithmic derivative.The aim of this paper is to compare these two versions of quantum Fisher information,and to establish two informational inequalities relating them.
International Symposium on Information Theory and its Applications(ISITA2008), Auckland, New Zealand, 7-10, December, 2008 -- (Abstract)We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cram´er-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.
In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance: The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom's study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper is to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.