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

Communications in Theoretical Physics

Entanglement of Formation for Quantum States

Hui Zhao, Zhi‐Xi Wang

Published Jan 1, 2007• 3 citations
Publisher

Abstract

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generalized concurrence. From the monotonicity and convexity the entanglement of formation for a class of high-dimensional mixed states has been calculated analytically.

DOI
10.1088/0253-6102/47/1/010

Related papers

Entanglement of formation and concurrence for mixed states

Xiu-Hong Gao, Sergio A Albeverio, Kai Chen +2 more

We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.

Frontiers of Computer Science in China•Jun 1, 2008•27 citations

ENTANGLEMENT OF FORMATION FOR A CLASS OF SPECIAL QUANTUM STATES

Hui Zhao, Zhi‐Xi Wang

The entanglement of formation for a class of high-dimensional quantum mixed states is investigated. A special kind of D-computable states is defined and the lower bound of entanglement of formation for a large class of density matrices whose decompositions lie in these D-computable quantum states is obtained. Moreover we present a kind of construction for this special state which is defined by a class of special matrices with two non-zero different eigenvalues and the other eigenvalues are zero. Making use of the D-computable we construct a class of bound entangled states.

International Journal of Quantum Information•May 30, 2007•2 citations

Entanglement of formation for a family of (2⊗d) -dimensional systems

F. Lastra, C. E. López, Luis Roa +1 more

Entanglement of formation for arbitrary mixed states in a ($2\ensuremath{\bigotimes}2$)-dimensional Hilbert space is well known. For higher-dimensional mixed states analytical expressions for quantifying entanglement exist for a particular family of states. In this work, we calculate analytically the entanglement of formation for a family of bipartite ($2\ensuremath{\bigotimes}d$)-dimensional mixed states which can be obtained from tripartite $2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}d$ pure states following the entanglement relations obtained by Koashi and Winter [Phys. Rev. A 69, 022309 (2004)].

arXiv:1105.6321•Physical Review A•Feb 15, 2012•18 citations

A note on invariants and entanglements

Sergio A Albeverio, Shao-Ming Fei

Quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for N -dimensional quantum systems is presented. This generalized concurrence has potential applications in studying separability and calculating the entanglement of formation for high-dimensional mixed quantum states.

arXiv:quant-ph/0109073•Journal of Optics B Quantum and Semiclassical Optics•Jul 9, 2001•187 citations

Simulated annealing and entanglement of formation for (n⊗m) -dimensional mixed states

S. Allende, D. Altbir, J. C. Retamal

The simulated annealing algorithm, a method commonly used to calculate properties of condensed-matter systems, is used to calculate entanglement of formation for higher-dimensional mixed states. The method relies on representing a mixed state as a pure state in an enlarged Hilbert space, and on the search for the extension minimizing the convex roof of entanglement of formation. Exact results are found, and predictions for system reservoir dynamics in higher dimensions are confirmed. These findings open the way for new applications of the method in quantum information.

Physical Review A•Aug 24, 2015•7 citations

On properties of the space of quantum states and their application to the construction of entanglement monotones

Максим Евгеньевич Широков

We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the resulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.

arXiv:0804.1515•Izvestiya Mathematics•Sep 7, 2010•32 citations
We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generalized concurrence. From the monotonicity and convexity the entanglement of formation for a class of high-dimensional mixed states has been calculated analytically.
The entanglement of formation for a class of high-dimensional quantum mixed states is investigated. A special kind of D-computable states is defined and the lower bound of entanglement of formation for a large class of density matrices whose decompositions lie in these D-computable quantum states is obtained. Moreover we present a kind of construction for this special state which is defined by a class of special matrices with two non-zero different eigenvalues and the other eigenvalues are zero. Making use of the D-computable we construct a class of bound entangled states.
Entanglement of formation for arbitrary mixed states in a ($2\ensuremath{\bigotimes}2$)-dimensional Hilbert space is well known. For higher-dimensional mixed states analytical expressions for quantifying entanglement exist for a particular family of states. In this work, we calculate analytically the entanglement of formation for a family of bipartite ($2\ensuremath{\bigotimes}d$)-dimensional mixed states which can be obtained from tripartite $2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}d$ pure states following the entanglement relations obtained by Koashi and Winter [Phys. Rev. A 69, 022309 (2004)].
The simulated annealing algorithm, a method commonly used to calculate properties of condensed-matter systems, is used to calculate entanglement of formation for higher-dimensional mixed states. The method relies on representing a mixed state as a pure state in an enlarged Hilbert space, and on the search for the extension minimizing the convex roof of entanglement of formation. Exact results are found, and predictions for system reservoir dynamics in higher dimensions are confirmed. These findings open the way for new applications of the method in quantum information.
We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the resulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.