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

Caculating the relative entropy of entanglement

Shengjun Wu, Yongde Zhang

Published Apr 5, 2000• 0 citations
OpenAlex

Abstract

We extend Vedral and Plenio's theorem (theorem 3 in Phys. Rev. A 57, 1619) to a more general case, and obtain the relative entropy of entanglement for a class of mixed states.

Related papers

Relative Entropy and Relative Entropy of Entanglement for Infinite-Dimensional Systems

Zhoubo Duan, Lifang Niu, Yangyang Wang +1 more

International Journal of Theoretical Physics•Apr 6, 2017•8 citations

Two Theorems on Calculating the Relative Entropy of Entanglement

Shengjun Wu, Wu Qiang, Zhang Yong-De

We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.

arXiv:quant-ph/0004018•Chinese Physics Letters•Feb 1, 2001•12 citations

Relative Entropy of Entanglement of One Class of Two-Qubit System

Lin-Mei Liang, Ping‐Xing Chen, Cheng-Zu Li +1 more

The relative entropy of entanglement of a mixed state σ for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states. Vedral et al. [Phys. Rev. A 57(1998)1619] have recently proposed a numerical method to obtain the relative entropy of entanglement E re for two-qubit systems. This letter shows that the convex programming method can be applied to calculate E re of two-qubit systems analytically, and discusses the conditions under which the method can be adopted.

Chinese Physics Letters•Feb 8, 2001•12 citations

New Additivity Properties of the Relative Entropy of Entanglement and Its Generalizations

Roberto Rubboli, Marco Tomamichel

arXiv:2211.12804•Communications in Mathematical Physics•Jun 23, 2024•11 citations

Generalized entanglement measure for continuous-variable systems

S. Nibedita Swain, Vineeth S. Bhaskara, Prasanta Kumar Panigrahi

Concurrence, introduced by Hill and Wootters [Hill and Wootters, Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of the entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Bhaskara and Panigrahi, Quantum Inf. Process. 16, 118 (2017)] for pure discrete-variable systems in arbitrary dimensions and extending the concept to mixed continuous-variable states. A family of faithful entanglement measures is constructed that admits necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Vedral, Plenio, Rippin, and Knight, Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states, and non-Gaussian continuous-variable Bell states matches with known results. We also quantify entanglement of phase-randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.

arXiv:1706.01448•Physical Review A•May 27, 2022•11 citations

Relative entropy of entanglement of rotationally invariant states

Zhen Wang, Zhixi Wang

arXiv:0812.0074•Physics Letters A•Oct 18, 2008•9 citations
The relative entropy of entanglement of a mixed state σ for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states. Vedral et al. [Phys. Rev. A 57(1998)1619] have recently proposed a numerical method to obtain the relative entropy of entanglement E re for two-qubit systems. This letter shows that the convex programming method can be applied to calculate E re of two-qubit systems analytically, and discusses the conditions under which the method can be adopted.
Concurrence, introduced by Hill and Wootters [Hill and Wootters, Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of the entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Bhaskara and Panigrahi, Quantum Inf. Process. 16, 118 (2017)] for pure discrete-variable systems in arbitrary dimensions and extending the concept to mixed continuous-variable states. A family of faithful entanglement measures is constructed that admits necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Vedral, Plenio, Rippin, and Knight, Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states, and non-Gaussian continuous-variable Bell states matches with known results. We also quantify entanglement of phase-randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.