Evaluation of two different entanglement measures on a bound entangled state

TL;DR

This paper compares two entanglement measures on a specific three-qubit bound entangled state, providing explicit calculations and insights into their effectiveness in characterizing such complex quantum states.

Contribution

It introduces a method to compute entanglement measures on a bound entangled state using a basis of minimally-entangled states, with explicit results for geometric measure and generalized concurrence.

Findings

Explicit values for geometric measure and generalized concurrence.

Demonstrates the applicability of the method to bound entangled states.

Provides insights into the effectiveness of different entanglement measures.

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.