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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 301072, 57 pages
Review Article

Quantum Entanglement: Separability, Measure, Fidelity of Teleportation, and Distillation

1College of Mathematics and Computational Science, China University of Petroleum, 257061 Dongying, China
2Department of Mathematics, Capital Normal University, 100037 Beijing, China
3Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

Received 29 August 2009; Accepted 2 December 2009

Academic Editor: NaiHuan Jing

Copyright © 2010 Ming Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Quantum entanglement plays crucial roles in quantum information processing. Quantum entangled states have become the key ingredient in the rapidly expanding field of quantum information science. Although the nonclassical nature of entanglement has been recognized for many years, considerable efforts have been taken to understand and characterize its properties recently. In this review, we introduce some recent results in the theory of quantum entanglement. In particular separability criteria based on the Bloch representation, covariance matrix, normal form and entanglement witness, lower bounds, subadditivity property of concurrence and tangle, fully entangled fraction related to the optimal fidelity of quantum teleportation, and entanglement distillation will be discussed in detail.