Evaluation of two different entanglement measures on a bound entangled state

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.