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:1104.1006

Detecting the concurrence of an unknown state with a single observable

Zhihao Ma, Zhihua Chen, Jing‐Ling Chen

Published Apr 6, 2011• 0 citations
arXivHTMLPDF

Abstract

While the detection of entanglement has been proved already to be quite a difficult task, experimental quantification of entanglement is even more challenging. In this work, we derive an analytical lower bound for the concurrence of a bipartite mix quantum state in arbitrary dimension. The lower bound is experimentally implementable in a feasible way, which enabling quantification of entanglement in a broad variety of cases

DOI
10.48550/arxiv.1104.1006

Related papers

A note on lower bounds of concurrence for arbitrary dimensional bipartite quantum states

Zhi-Bo Chen, Shao-Ming Fei

Abstract Quantification of quantum entanglement plays a crucial role in the study of quantum information tasks. We present analytical lower bounds for both concurrence and 2-concurrence based on the correlation matrices of bipartite quantum states. Compared with other related lower bounds, our approach provides a better estimation of the entanglement, particularly for states with large purity.

arXiv:2503.16291•Laser Physics•Mar 18, 2025•1 citation

A lower bound of concurrence for multipartite quantum states

Ming Li, Shao-Ming Fei, Zhi‐Xi Wang

We study the concurrence of arbitrary multipartite mixed quantum states. An explicit lower bound of the concurrence is derived, which detects quantum entanglement of some states better than some separability criteria, and gives sufficient conditions for distilling GHZ states from tripartite states. An interesting relation between the lower bound of the concurrence for bipartite states and for tripartite states has been presented.

arXiv:0903.3145•Journal of Physics A Mathematical and Theoretical•Mar 17, 2009•59 citations

Concurrence of Arbitrary Dimensional Bipartite Quantum States

Kai Chen, Sergio A Albeverio, Shao-Ming Fei

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.

arXiv:quant-ph/0506136•Physical Review Letters•Jul 22, 2005•315 citations

Measure of genuine multipartite entanglement with computable lower bounds

Zhihao Ma, Zhihua Chen, Jing‐Ling Chen +3 more

We introduce an intuitive measure of genuine multipartite entanglement, which is based on the well-known concurrence. We show how lower bounds on this measure can be derived and also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.

arXiv:1101.2001•Physical Review A•Jun 20, 2011•300 citations

Lower bound of concurrence based on positive maps

Xiaosheng Li, Xiu-Hong Gao, Shao-Ming Fei

We study the concurrence of arbitrary dimensional bipartite quantum systems. An explicit analytical lower bound of concurrence is obtained which detects entanglement for some quantum states better than some well-known separability criteria and improves the lower bounds, such as from the positive partial transposition, realignment criteria, and Breuer's entanglement witness.

arXiv:1104.1000•Physical Review A•Mar 25, 2011•17 citations

Quantifying Entanglement of Maximal Dimension in Bipartite Mixed States

Gael Sentís, Christopher Eltschka, Otfried Gühne +2 more

The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the forms of entanglement that can only exist in high-dimensional systems. We derive a framework for lower bounding the appropriate measure of entanglement, the so-called G-concurrence, through few local measurements. Moreover, we show that these bounds have relevant applications also for multipartite states.

arXiv:1605.09783•Physical Review Letters•Nov 4, 2016•25 citations
While the detection of entanglement has been proved already to be quite a difficult task, experimental quantification of entanglement is even more challenging. In this work, we derive an analytical lower bound for the concurrence of a bipartite mix quantum state in arbitrary dimension. The lower bound is experimentally implementable in a feasible way, which enabling quantification of entanglement in a broad variety of cases
We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the forms of entanglement that can only exist in high-dimensional systems. We derive a framework for lower bounding the appropriate measure of entanglement, the so-called G-concurrence, through few local measurements. Moreover, we show that these bounds have relevant applications also for multipartite states.