2010Physical Review AOpen access

Evaluation of two different entanglement measures on a bound entangled state

Cyril Branciard, Huangjun Zhu, Lin Chen, Valerio Scarani

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Abstract

We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an unextendible product basis [C. H. Bennett et al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact that no product state lies in the support of that state, we compute its entanglement by providing a basis of its subspace formed by ``minimally entangled'' states. The approach is in principle applicable to any entanglement measure; here we provide explicit values for both the geometric measure of entanglement and a generalized concurrence.

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We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an unextendible product basis [C. H. Bennett et al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact that no product state lies in the support of that state, we compute its entanglement by providing a basis of its subspace formed by ``minimally entangled'' states. The approach is in principle applicable to any entanglement measure; here we provide explicit values for both the geometric measure of entanglement and a generalized concurrence.

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Available abstract

We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an unextendible product basis [C. H. Bennett et al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact that no product state lies in the support of that state, we compute its entanglement by providing a basis of its subspace formed by ``minimally entangled'' states. The approach is in principle applicable to any entanglement measure; here we provide explicit values for both the geometric measure of entanglement and a generalized concurrence.

Key concepts: Quantum entanglement, Measure (data warehouse), Concurrence, Basis (linear algebra), Multipartite entanglement, Subspace topology, W state, Squashed entanglement

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