Frontiers of Computer Science in China

Entanglement of formation and concurrence for mixed states

Xiu-Hong Gao, Sergio A Albeverio, Kai Chen, Shao-Ming Fei, Xianqing Li‐Jost

Published Jun 1, 2008• 27 citations

Abstract

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.

DOI: 10.1007/s11704-008-0017-8

Related papers

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:0903.3145Journal of Physics A Mathematical and TheoreticalMar 17, 200959 citations

Improved lower and upper bounds for entanglement of formation

Xue‐Na Zhu, Shao-Ming Fei

We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed examples are presented.

arXiv:1211.0464Physical Review ANov 1, 201214 citations

Evolution of entanglement for quantum mixed states

Chang‐shui Yu, X. X. Yi, He‐Shan Song

A simple relation is introduced for concurrence to describe how much the entanglement of a bipartite system is at least left if either (or both) subsystem undergoes an arbitrary physical process. This provides a lower bound for concurrence of mixed states (pure states are included) in contrast to the upper bound given by Konrad et al. [Nat. Phys. 4, 99 (2008)]. Our results are also suitable for general high-dimensional bipartite quantum systems.

arXiv:0812.3959Physical Review ADec 18, 200825 citations

Estimation of concurrence for multipartite mixed states

Xiaoting Gao, S.-M. Fei

We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.

The European Physical Journal Special TopicsMay 20, 200845 citations

Review of Entanglement of Formation and Concurrence of bipartite systems

Riya Sett

Quantum information and computation is one of the new fields of physics and information science. Entanglement is one of the most significant resources in quantum information processing. The most basic quantitative measure of entanglement, particularly for mixed states of a bipartite system is the entanglement of formation. This entanglement of formation is used in the concurrence, another measurement of entanglement. Here I have briefly reviewed the entanglement of formation and the concurrence of bipartite systems. I have discussed that for a three qubit pure state, if A, B and C are the three qubits, then sum of the squared concurrence between A and B and the squared concurrence between A and C never exceeds the squared concurrence between A and BC pair. The residual entanglement, obtained from the aforementioned inequality, is also discussed here. Keywords- Quantum information, entanglement, qubit.

American Journal of Electronics & CommunicationOct 3, 20150 citations

Lower bound of multipartite concurrence based on subquantum state decomposition

Xue‐Na Zhu, Ming‐Jing Zhao, Shao-Ming Fei

We study the entanglement of tripartite quantum states and provide analytical lower bounds of concurrence in terms of the concurrence of substates. The lower bound may improve all of the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.

arXiv:1208.1745Physical Review AAug 7, 201212 citations