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:quant-ph/0412092 · Physical Review A

Wigner-Yanase skew information as tests for quantum entanglement

Zeqian Chen

Published May 3, 2005• 74 citations
arXivHTMLPDF

Abstract

A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.

DOI
10.1103/physreva.71.052302

Related papers

Multipartite entanglement detection via generalized Wigner–Yanase skew information

Yan Hong, Yabin Xing, Limin Gao +2 more

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement,so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.

arXiv:2309.11034•Results in Physics•Mar 28, 2024•3 citations

Several families of entanglement criteria for multipartite quantum systems based on generalized Wigner-Yanase skew information and variance

Yan Hong, Hao, Xinlan, Limin Gao

Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information $I^s(ρ,X)$ for $-1\leq s\leq0$ and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.

arXiv:2409.11273•Sep 17, 2024•0 citations

Concurrence and Wigner–Yanase Skew Information

Li Tang, Zeqian Chen

A measure of entanglement on n qubits is defined in terms of Wigner–Yanase skew information. It is shown that the measure coincides essentially with the concurrence on two qubits. This uncovers the information-theoretic meaning of the concurrence of entangled states.

Chinese Physics Letters•Feb 24, 2006•7 citations

Generalized Wigner-Yanase skew information and the affiliated inequality

Ma-Cheng Yang, Cong‐Feng Qiao

A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is given, implying a simple proof of the Wigner-Yanase-Dyson conjecture. We find in this work an exact skew information inequality for a qubit system, which may be regarded as the information counterpart of the uncertainty relation. A lower bound for the generalized skew information of a pair of incompatible observables in arbitrary dimension and also the upper bound for a qubit system are achieved.

arXiv:2205.06988•Physical Review A•Nov 1, 2022•11 citations

Several families of entanglement criteria for multipartite quantum systems based on the generalized Wigner–Yanase skew information and variance

Yan Hong, Xinlan Hao, Limin Gao

Abstract Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner–Yanase skew information I s ( ρ , X ) for − 1 ⩽ s ⩽ 0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner–Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.

Laser Physics Letters•Nov 6, 2024•1 citation

Quantifying correlations via the Wigner-Yanase skew information

Shunlong Luo, Shuangshuang Fu, Choo Hiap Oh

In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.

Physical Review A•Mar 15, 2012•108 citations
A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.
The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate kkk-nonseparability and kkk-partite entanglement of NNN-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang etetet alalal.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its kkk-nonseparability or kkk-partite entanglement,so these inequalities present the hierarchic classifications of kkk-nonseparability or kkk-partite entanglement for all NNN-partite quantum states from NNN-nonseparability to 222-nonseparability or from 222-partite entanglement to NNN-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some kkk-nonseparability and kkk-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.
Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information Is(ρ,X)I^s(ρ,X)Is(ρ,X) for −1≤s≤0-1\leq s\leq0−1≤s≤0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is given, implying a simple proof of the Wigner-Yanase-Dyson conjecture. We find in this work an exact skew information inequality for a qubit system, which may be regarded as the information counterpart of the uncertainty relation. A lower bound for the generalized skew information of a pair of incompatible observables in arbitrary dimension and also the upper bound for a qubit system are achieved.
Abstract Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner–Yanase skew information I s ( ρ , X ) for − 1 ⩽ s ⩽ 0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner–Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.
In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.