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:0812.2877 · Quantum Information Processing

Entanglement of formation is non-monotonic with concurrence: a simple proof

Indrani Chattopadhyay, Debasis Sarkar

Published Oct 30, 2008• 7 citations
arXivHTMLPDF
DOI
10.1007/s11128-008-0085-6

Related papers

A note on entanglement of formation and generalized concurrence

Shao-Ming Fei, Zhi‐Xi Wang, Hui Zhao

arXiv:quant-ph/0408131•Physics Letters A•Aug 4, 2004•34 citations

Entanglement of Formation for Quantum States

Hui Zhao, Zhi‐Xi Wang

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.

Communications in Theoretical Physics•Jan 1, 2007•3 citations

Tripartite entanglement measure under local operations and classical communication

Xiaozhen Ge, Lijun Liu, Shuming Cheng

Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.

arXiv:2210.06700•Physical Review A•Mar 7, 2023•25 citations

Towards Additivity of Entanglement of Formation

Toshiyuki Shimono

Lecture notes in computer science•Jan 1, 2002•1 citation

On Strong Superadditivity of the Entanglement of Formation

Koenraad M.R. Audenaert, Samuel L. Braunstein

arXiv:quant-ph/0303045•Communications in Mathematical Physics•Apr 1, 2004•39 citations

Constructing Frameness Monotones For Dephasing Channels

Borzu Toloui, Gilad Gour, Barry C. Sanders

Restrictions on quantum operations give rise to resource theories. Total lack of a shared reference frame for transformations associated with a group G between two parties is equivalent to having, in effect, an invariant channel between the parties and a corresponding superselection rule. The resource associated with the absence of the reference frame is known as or asymmetry. We show that any entanglement monotone for pure bipartite states can be adapted as a pure-state monotone for phase-invariant channels [equivalently U(1) superselection rules] and extended to the case of mixed states via the convex-roof extension. As an application, we construct a family of concurrence monotones for U(1) for general finite-dimensional Hilbert spaces. Furthermore, we study frameness of formation for mixed states analogous to entanglement of formation. In the case of a qubit, we show that it can be expressed as an analytical function of the concurrence analogously to the Wootters formula for entanglement of formation. Our results highlight deep links between entanglement and resource theories.

•Apr 6, 2011•0 citations
Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.
Restrictions on quantum operations give rise to resource theories. Total lack of a shared reference frame for transformations associated with a group G between two parties is equivalent to having, in effect, an invariant channel between the parties and a corresponding superselection rule. The resource associated with the absence of the reference frame is known as or asymmetry. We show that any entanglement monotone for pure bipartite states can be adapted as a pure-state monotone for phase-invariant channels [equivalently U(1) superselection rules] and extended to the case of mixed states via the convex-roof extension. As an application, we construct a family of concurrence monotones for U(1) for general finite-dimensional Hilbert spaces. Furthermore, we study frameness of formation for mixed states analogous to entanglement of formation. In the case of a qubit, we show that it can be expressed as an analytical function of the concurrence analogously to the Wootters formula for entanglement of formation. Our results highlight deep links between entanglement and resource theories.