Concurrence as a Relative Entropy with Hilbert-Schmidt Distance in Bell Decomposable States

Akhtarshenas, S. J.; Jafarizadeh, M. A.

Concurrence as a Relative Entropy with Hilbert-Schmidt Distance in Bell Decomposable States

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Description

Hilbert-Schmidt distance reduces to Euclidean distance in Bell decomposable states. Based on this, entanglement of these states are obtained according to the protocol proposed in Ref. [V. Vedral et al, Phys. Rev. Lett. 78, 2275 (1995)] with Hilbert-Schmidt distance. It is shown that this measure is equal to the concurrence and thus can be used to generate entanglement of formation. We also introduce a new measure of distance and show that under the action of restricted LQCC operations, the associated measure of entanglement transforms in the same way as the concurrence transforms .
14 pages, Latex